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Trigonometry Formulas:

LIST OF PAGE CONTENT

  • Definition of Trigonometric functions
  • Inter Relations Between Trigonometric Functions
  • Values of Trigonometric Ratios for certain standard angles
  • Pythagorean Identities
  • Even/Odd Identities
  • Periodic Identities
  • Trigonometric Ratios Of Compound Angles
  • Double Angle Formulas
  • Multiple Angle Formulas
  • Power Reduction Formulas
  • Half Angle Formulas
  • Product To Sum Formulas
  • Sum To Product Formulas
    • Definition of Trigonometric functions
    X-axisY-axisθxyrp(x,y) x = adjacent sidey = opposite sider = hypotenusewww.faastop.com الله π X-axisY-axisθxyrp(x,y) x = adjacent sidey = opposite sider = hypotenuseX-axisY-axisθxyrp(x,y) x = adjacent sidey = opposite sider = hypotenuse
    𝑠𝑖𝑛(θ) = opposite sidehypotenuse   = ——𝑦𝑟 www.faastop.comاللهπ𝑠𝑖𝑛(θ) = opposite sidehypotenuse   = ——𝑦𝑟 𝑠𝑖𝑛(θ) = opposite sidehypotenuse   = ——𝑦𝑟
    𝑐𝑜𝑠(θ) =adjacent sidehypotenuse   = ——x𝑟 www.faastop.comاللهπ𝑐𝑜𝑠(θ) =adjacent sidehypotenuse   = ——x𝑟 𝑐𝑜𝑠(θ) =adjacent sidehypotenuse   = ——x𝑟
    𝑡𝑎𝑛(θ) =opposite sideadjacent side   = ——𝑦x www.faastop.comاللهπ𝑡𝑎𝑛(θ) =opposite sideadjacent side   = ——𝑦x 𝑡𝑎𝑛(θ) =opposite sideadjacent side   = ——𝑦x
    𝑐𝑜𝑡(θ) = adjacent sideopposite side = ——x𝑦 www.faastop.comاللهπ𝑐𝑜𝑡(θ) = adjacent sideopposite side = ——x𝑦 𝑐𝑜𝑡(θ) = adjacent sideopposite side = ——x𝑦
    𝑐𝑜𝑠𝑒𝑐(θ) = hypotenuseopposite side = ——r𝑦 www.faastop.comاللهπ𝑐𝑜𝑠𝑒𝑐(θ) = hypotenuseopposite side = ——r𝑦 𝑐𝑜𝑠𝑒𝑐(θ) = hypotenuseopposite side = ——r𝑦
    𝑠𝑒𝑐(θ) = hypotenuseadjacent side = ——r x www.faastop.comاللهπ𝑠𝑒𝑐(θ) = hypotenuseadjacent side = ——r x 𝑠𝑒𝑐(θ) = hypotenuseadjacent side = ——r x
    Inter Relations Between Trigonometric Functions
    www.faastop.com الله π www.faastop.com الله π 𝑠𝑖𝑛(θ) =1𝑐𝑜𝑠𝑒𝑐(θ) (or) (or) 𝑐𝑜𝑠𝑒𝑐(θ) =1𝑠𝑖𝑛(θ) 𝑠𝑖𝑛(θ)𝑐𝑜𝑠𝑒𝑐(θ) = 1www.faastop.com الله π 𝑠𝑖𝑛(θ) =1𝑐𝑜𝑠𝑒𝑐(θ) (or) (or) 𝑠𝑖𝑛(θ) =1𝑐𝑜𝑠𝑒𝑐(θ) (or) (or) 𝑐𝑜𝑠𝑒𝑐(θ) =1𝑠𝑖𝑛(θ) 𝑠𝑖𝑛(θ)𝑐𝑜𝑠𝑒𝑐(θ) = 1 𝑐𝑜𝑠𝑒𝑐(θ) =1𝑠𝑖𝑛(θ)𝑠𝑖𝑛(θ) =1𝑐𝑜𝑠𝑒𝑐(θ) (or) (or) 𝑐𝑜𝑠𝑒𝑐(θ) =1𝑠𝑖𝑛(θ) 𝑠𝑖𝑛(θ)𝑐𝑜𝑠𝑒𝑐(θ) = 1 𝑠𝑖𝑛(θ)𝑐𝑜𝑠𝑒𝑐(θ) = 1𝑠𝑖𝑛(θ) =1𝑐𝑜𝑠𝑒𝑐(θ) (or) (or) 𝑐𝑜𝑠𝑒𝑐(θ) =1𝑠𝑖𝑛(θ) 𝑠𝑖𝑛(θ)𝑐𝑜𝑠𝑒𝑐(θ) = 1
    www.faastop.com الله π www.faastop.com الله π 𝑐𝑜𝑠(θ) =1𝑠𝑒𝑐(θ) (or) (or) 𝑠𝑒𝑐(θ) =1𝑐𝑜𝑠(θ)𝑠𝑒𝑐(θ)𝑐𝑜𝑠(θ) = 1www.faastop.com الله π 𝑐𝑜𝑠(θ) =1𝑠𝑒𝑐(θ) (or) (or) 𝑐𝑜𝑠(θ) =1𝑠𝑒𝑐(θ) (or) (or) 𝑠𝑒𝑐(θ) =1𝑐𝑜𝑠(θ)𝑠𝑒𝑐(θ)𝑐𝑜𝑠(θ) = 1 𝑠𝑒𝑐(θ) =1𝑐𝑜𝑠(θ)𝑐𝑜𝑠(θ) =1𝑠𝑒𝑐(θ) (or) (or) 𝑠𝑒𝑐(θ) =1𝑐𝑜𝑠(θ)𝑠𝑒𝑐(θ)𝑐𝑜𝑠(θ) = 1𝑠𝑒𝑐(θ)𝑐𝑜𝑠(θ) = 1𝑐𝑜𝑠(θ) =1𝑠𝑒𝑐(θ) (or) (or) 𝑠𝑒𝑐(θ) =1𝑐𝑜𝑠(θ)𝑠𝑒𝑐(θ)𝑐𝑜𝑠(θ) = 1
    www.faastop.com الله π www.faastop.com الله π 𝑡𝑎𝑛(θ) =1𝑐𝑜𝑡(θ) (or) (or) 𝑐𝑜𝑡(θ) =1𝑡𝑎𝑛(θ)𝑡𝑎𝑛(θ)𝑐𝑜𝑡(θ) = 1www.faastop.com الله π 𝑡𝑎𝑛(θ) =1𝑐𝑜𝑡(θ) (or) (or) 𝑡𝑎𝑛(θ) =1𝑐𝑜𝑡(θ) (or) (or) 𝑐𝑜𝑡(θ) =1𝑡𝑎𝑛(θ)𝑡𝑎𝑛(θ)𝑐𝑜𝑡(θ) = 1 𝑐𝑜𝑡(θ) =1𝑡𝑎𝑛(θ)𝑡𝑎𝑛(θ) =1𝑐𝑜𝑡(θ) (or) (or) 𝑐𝑜𝑡(θ) =1𝑡𝑎𝑛(θ)𝑡𝑎𝑛(θ)𝑐𝑜𝑡(θ) = 1𝑡𝑎𝑛(θ)𝑐𝑜𝑡(θ) = 1𝑡𝑎𝑛(θ) =1𝑐𝑜𝑡(θ) (or) (or) 𝑐𝑜𝑡(θ) =1𝑡𝑎𝑛(θ)𝑡𝑎𝑛(θ)𝑐𝑜𝑡(θ) = 1
    𝑡𝑎𝑛(θ) =𝑠𝑖𝑛(θ)𝑐𝑜𝑠(θ) www.faastop.com الله π 𝑡𝑎𝑛(θ) =𝑠𝑖𝑛(θ)𝑐𝑜𝑠(θ) 𝑡𝑎𝑛(θ) =𝑠𝑖𝑛(θ)𝑐𝑜𝑠(θ)
    𝑐𝑜𝑡(θ) =𝑐𝑜𝑠(θ)𝑠𝑖𝑛(θ) www.faastop.com الله π 𝑐𝑜𝑡(θ) =𝑐𝑜𝑠(θ)𝑠𝑖𝑛(θ) 𝑐𝑜𝑡(θ) =𝑐𝑜𝑠(θ)𝑠𝑖𝑛(θ)
    Values of T Ratios for certaiun standard angles
    www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π 01——21——√2√3——21 √3——21——√21——20-1——2-1-√3——20 1√3——21——√21——20 -1——2-1——√2-√3——2-1-√3——201——2  101——√31√3∞-√3-1-1——√301——√3 ∞-√30 ∞√311——√3 0 -1——√3 -1-√3 ∞ √3 0 -1——√3 ∞ ∞2√22——√3 1 2——√3√2 2 ∞ -2 -1-2——√3 ∞ 12——√3√22 ∞ -2-√2-2——√3 -1 -2——√3 ∞ 2  1 www.faastop.com الله π 01——21——√2√3——21 √3——21——√21——20-1——2-1-√3——20 01——21——√2√3——21 √3——21——√21——20-1——2-1-√3——20 1√3——21——√21——20 -1——2-1——√2-√3——2-1-√3——201——2  101——√31√3∞-√3-1-1——√301——√3 ∞-√30 ∞√311——√3 0 -1——√3 -1-√3 ∞ √3 0 -1——√3 ∞ ∞2√22——√3 1 2——√3√2 2 ∞ -2 -1-2——√3 ∞ 12——√3√22 ∞ -2-√2-2——√3 -1 -2——√3 ∞ 2  11√3——21——√21——20 -1——2-1——√2-√3——2-1-√3——201——2  101——21——√2√3——21 √3——21——√21——20-1——2-1-√3——20 1√3——21——√21——20 -1——2-1——√2-√3——2-1-√3——201——2  101——√31√3∞-√3-1-1——√301——√3 ∞-√30 ∞√311——√3 0 -1——√3 -1-√3 ∞ √3 0 -1——√3 ∞ ∞2√22——√3 1 2——√3√2 2 ∞ -2 -1-2——√3 ∞ 12——√3√22 ∞ -2-√2-2——√3 -1 -2——√3 ∞ 2  101——√31√3∞-√3-1-1——√301——√3 ∞-√3001——21——√2√3——21 √3——21——√21——20-1——2-1-√3——20 1√3——21——√21——20 -1——2-1——√2-√3——2-1-√3——201——2  101——√31√3∞-√3-1-1——√301——√3 ∞-√30 ∞√311——√3 0 -1——√3 -1-√3 ∞ √3 0 -1——√3 ∞ ∞2√22——√3 1 2——√3√2 2 ∞ -2 -1-2——√3 ∞ 12——√3√22 ∞ -2-√2-2——√3 -1 -2——√3 ∞ 2  1 ∞√311——√3 0 -1——√3 -1-√3 ∞ √3 0 -1——√3 ∞01——21——√2√3——21 √3——21——√21——20-1——2-1-√3——20 1√3——21——√21——20 -1——2-1——√2-√3——2-1-√3——201——2  101——√31√3∞-√3-1-1——√301——√3 ∞-√30 ∞√311——√3 0 -1——√3 -1-√3 ∞ √3 0 -1——√3 ∞ ∞2√22——√3 1 2——√3√2 2 ∞ -2 -1-2——√3 ∞ 12——√3√22 ∞ -2-√2-2——√3 -1 -2——√3 ∞ 2  1 ∞2√22——√3 1 2——√3√2 2 ∞ -2 -1-2——√3 ∞01——21——√2√3——21 √3——21——√21——20-1——2-1-√3——20 1√3——21——√21——20 -1——2-1——√2-√3——2-1-√3——201——2  101——√31√3∞-√3-1-1——√301——√3 ∞-√30 ∞√311——√3 0 -1——√3 -1-√3 ∞ √3 0 -1——√3 ∞ ∞2√22——√3 1 2——√3√2 2 ∞ -2 -1-2——√3 ∞ 12——√3√22 ∞ -2-√2-2——√3 -1 -2——√3 ∞ 2  1 12——√3√22 ∞ -2-√2-2——√3 -1 -2——√3 ∞ 2  101——21——√2√3——21 √3——21——√21——20-1——2-1-√3——20 1√3——21——√21——20 -1——2-1——√2-√3——2-1-√3——201——2  101——√31√3∞-√3-1-1——√301——√3 ∞-√30 ∞√311——√3 0 -1——√3 -1-√3 ∞ √3 0 -1——√3 ∞ ∞2√22——√3 1 2——√3√2 2 ∞ -2 -1-2——√3 ∞ 12——√3√22 ∞ -2-√2-2——√3 -1 -2——√3 ∞ 2  1𝑠𝑖𝑛(θ) θ→T Ratio↓𝑠𝑖𝑛θ𝑐𝑜𝑠θ𝑡𝑎𝑛θ𝑐𝑜𝑡θ𝑐𝑜𝑠𝑒𝑐θ𝑠𝑒𝑐θ0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6 π 7π/6 3π/2 5π/3 2π0⁰ 30⁰ 45⁰ 60⁰ 90⁰ 120⁰ 135⁰ 150⁰ 180⁰ 210⁰ 270⁰ 300⁰ 360⁰
    Pythagorean Identities
    www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π 𝑠𝑖𝑛²θ + 𝑐𝑜𝑠²θ = 1 ,  ∀ θ ∈ ℝ Corollaries:——————𝑠𝑖𝑛²θ = 1-𝑐𝑜𝑠²θ 𝑠𝑖𝑛θ =  1-𝑐𝑜𝑠²θ 𝑐𝑜𝑠²θ = 1-𝑠𝑖𝑛²θ 𝑐𝑜𝑠θ =  1-𝑠𝑖𝑛²θ www.faastop.com الله π 𝑠𝑖𝑛²θ + 𝑐𝑜𝑠²θ = 1 ,  ∀ θ ∈ ℝ Corollaries:——————𝑠𝑖𝑛²θ + 𝑐𝑜𝑠²θ = 1 ,  ∀ θ ∈ ℝ Corollaries:——————𝑠𝑖𝑛²θ = 1-𝑐𝑜𝑠²θ 𝑠𝑖𝑛θ =  1-𝑐𝑜𝑠²θ 𝑐𝑜𝑠²θ = 1-𝑠𝑖𝑛²θ 𝑐𝑜𝑠θ =  1-𝑠𝑖𝑛²θ 𝑠𝑖𝑛²θ = 1-𝑐𝑜𝑠²θ 𝑠𝑖𝑛²θ + 𝑐𝑜𝑠²θ = 1 ,  ∀ θ ∈ ℝ Corollaries:——————𝑠𝑖𝑛²θ = 1-𝑐𝑜𝑠²θ 𝑠𝑖𝑛θ =  1-𝑐𝑜𝑠²θ 𝑐𝑜𝑠²θ = 1-𝑠𝑖𝑛²θ 𝑐𝑜𝑠θ =  1-𝑠𝑖𝑛²θ 𝑠𝑖𝑛θ =  1-𝑐𝑜𝑠²θ 𝑠𝑖𝑛²θ + 𝑐𝑜𝑠²θ = 1 ,  ∀ θ ∈ ℝ Corollaries:——————𝑠𝑖𝑛²θ = 1-𝑐𝑜𝑠²θ 𝑠𝑖𝑛θ =  1-𝑐𝑜𝑠²θ 𝑐𝑜𝑠²θ = 1-𝑠𝑖𝑛²θ 𝑐𝑜𝑠θ =  1-𝑠𝑖𝑛²θ 𝑐𝑜𝑠²θ = 1-𝑠𝑖𝑛²θ 𝑠𝑖𝑛²θ + 𝑐𝑜𝑠²θ = 1 ,  ∀ θ ∈ ℝ Corollaries:——————𝑠𝑖𝑛²θ = 1-𝑐𝑜𝑠²θ 𝑠𝑖𝑛θ =  1-𝑐𝑜𝑠²θ 𝑐𝑜𝑠²θ = 1-𝑠𝑖𝑛²θ 𝑐𝑜𝑠θ =  1-𝑠𝑖𝑛²θ 𝑐𝑜𝑠θ =  1-𝑠𝑖𝑛²θ 𝑠𝑖𝑛²θ + 𝑐𝑜𝑠²θ = 1 ,  ∀ θ ∈ ℝ Corollaries:——————𝑠𝑖𝑛²θ = 1-𝑐𝑜𝑠²θ 𝑠𝑖𝑛θ =  1-𝑐𝑜𝑠²θ 𝑐𝑜𝑠²θ = 1-𝑠𝑖𝑛²θ 𝑐𝑜𝑠θ =  1-𝑠𝑖𝑛²θ
    www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π 1+𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ,    ∀ θ ∈ ℝ -{(2𝑛+1)π/2|𝑛∈ℤ}Corollaries:——————𝑠𝑒𝑐²θ - 𝑡𝑎𝑛²θ = 1𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ - 1𝑡𝑎𝑛θ =   𝑠𝑒𝑐²θ-1 𝑠𝑒𝑐θ =   1+𝑡𝑎𝑛²θ (𝑠𝑒𝑐θ - 𝑡𝑎𝑛θ)(𝑠𝑒𝑐θ + 𝑡𝑎𝑛θ)=1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ =1𝑠𝑒𝑐θ+𝑡𝑎𝑛θ 𝑠𝑒𝑐θ+𝑡𝑎𝑛θ = 1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ www.faastop.com الله π 1+𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ,    ∀ θ ∈ ℝ -{(2𝑛+1)π/2|𝑛∈ℤ}Corollaries:——————1+𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ,    ∀ θ ∈ ℝ -{(2𝑛+1)π/2|𝑛∈ℤ}Corollaries:——————𝑠𝑒𝑐²θ - 𝑡𝑎𝑛²θ = 1𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ - 1𝑡𝑎𝑛θ =   𝑠𝑒𝑐²θ-1 𝑠𝑒𝑐θ =   1+𝑡𝑎𝑛²θ (𝑠𝑒𝑐θ - 𝑡𝑎𝑛θ)(𝑠𝑒𝑐θ + 𝑡𝑎𝑛θ)=1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ =1𝑠𝑒𝑐θ+𝑡𝑎𝑛θ 𝑠𝑒𝑐θ+𝑡𝑎𝑛θ = 1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ 𝑠𝑒𝑐²θ - 𝑡𝑎𝑛²θ = 11+𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ,    ∀ θ ∈ ℝ -{(2𝑛+1)π/2|𝑛∈ℤ}Corollaries:——————𝑠𝑒𝑐²θ - 𝑡𝑎𝑛²θ = 1𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ - 1𝑡𝑎𝑛θ =   𝑠𝑒𝑐²θ-1 𝑠𝑒𝑐θ =   1+𝑡𝑎𝑛²θ (𝑠𝑒𝑐θ - 𝑡𝑎𝑛θ)(𝑠𝑒𝑐θ + 𝑡𝑎𝑛θ)=1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ =1𝑠𝑒𝑐θ+𝑡𝑎𝑛θ 𝑠𝑒𝑐θ+𝑡𝑎𝑛θ = 1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ 𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ - 11+𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ,    ∀ θ ∈ ℝ -{(2𝑛+1)π/2|𝑛∈ℤ}Corollaries:——————𝑠𝑒𝑐²θ - 𝑡𝑎𝑛²θ = 1𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ - 1𝑡𝑎𝑛θ =   𝑠𝑒𝑐²θ-1 𝑠𝑒𝑐θ =   1+𝑡𝑎𝑛²θ (𝑠𝑒𝑐θ - 𝑡𝑎𝑛θ)(𝑠𝑒𝑐θ + 𝑡𝑎𝑛θ)=1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ =1𝑠𝑒𝑐θ+𝑡𝑎𝑛θ 𝑠𝑒𝑐θ+𝑡𝑎𝑛θ = 1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ 𝑡𝑎𝑛θ =   𝑠𝑒𝑐²θ-1 1+𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ,    ∀ θ ∈ ℝ -{(2𝑛+1)π/2|𝑛∈ℤ}Corollaries:——————𝑠𝑒𝑐²θ - 𝑡𝑎𝑛²θ = 1𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ - 1𝑡𝑎𝑛θ =   𝑠𝑒𝑐²θ-1 𝑠𝑒𝑐θ =   1+𝑡𝑎𝑛²θ (𝑠𝑒𝑐θ - 𝑡𝑎𝑛θ)(𝑠𝑒𝑐θ + 𝑡𝑎𝑛θ)=1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ =1𝑠𝑒𝑐θ+𝑡𝑎𝑛θ 𝑠𝑒𝑐θ+𝑡𝑎𝑛θ = 1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ 𝑠𝑒𝑐θ =   1+𝑡𝑎𝑛²θ 1+𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ,    ∀ θ ∈ ℝ -{(2𝑛+1)π/2|𝑛∈ℤ}Corollaries:——————𝑠𝑒𝑐²θ - 𝑡𝑎𝑛²θ = 1𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ - 1𝑡𝑎𝑛θ =   𝑠𝑒𝑐²θ-1 𝑠𝑒𝑐θ =   1+𝑡𝑎𝑛²θ (𝑠𝑒𝑐θ - 𝑡𝑎𝑛θ)(𝑠𝑒𝑐θ + 𝑡𝑎𝑛θ)=1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ =1𝑠𝑒𝑐θ+𝑡𝑎𝑛θ 𝑠𝑒𝑐θ+𝑡𝑎𝑛θ = 1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ (𝑠𝑒𝑐θ - 𝑡𝑎𝑛θ)(𝑠𝑒𝑐θ + 𝑡𝑎𝑛θ)=11+𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ,    ∀ θ ∈ ℝ -{(2𝑛+1)π/2|𝑛∈ℤ}Corollaries:——————𝑠𝑒𝑐²θ - 𝑡𝑎𝑛²θ = 1𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ - 1𝑡𝑎𝑛θ =   𝑠𝑒𝑐²θ-1 𝑠𝑒𝑐θ =   1+𝑡𝑎𝑛²θ (𝑠𝑒𝑐θ - 𝑡𝑎𝑛θ)(𝑠𝑒𝑐θ + 𝑡𝑎𝑛θ)=1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ =1𝑠𝑒𝑐θ+𝑡𝑎𝑛θ 𝑠𝑒𝑐θ+𝑡𝑎𝑛θ = 1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ 𝑠𝑒𝑐θ-𝑡𝑎𝑛θ =1𝑠𝑒𝑐θ+𝑡𝑎𝑛θ 1+𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ,    ∀ θ ∈ ℝ -{(2𝑛+1)π/2|𝑛∈ℤ}Corollaries:——————𝑠𝑒𝑐²θ - 𝑡𝑎𝑛²θ = 1𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ - 1𝑡𝑎𝑛θ =   𝑠𝑒𝑐²θ-1 𝑠𝑒𝑐θ =   1+𝑡𝑎𝑛²θ (𝑠𝑒𝑐θ - 𝑡𝑎𝑛θ)(𝑠𝑒𝑐θ + 𝑡𝑎𝑛θ)=1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ =1𝑠𝑒𝑐θ+𝑡𝑎𝑛θ 𝑠𝑒𝑐θ+𝑡𝑎𝑛θ = 1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ 𝑠𝑒𝑐θ+𝑡𝑎𝑛θ = 1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ 1+𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ,    ∀ θ ∈ ℝ -{(2𝑛+1)π/2|𝑛∈ℤ}Corollaries:——————𝑠𝑒𝑐²θ - 𝑡𝑎𝑛²θ = 1𝑡𝑎𝑛²θ = 𝑠𝑒𝑐²θ - 1𝑡𝑎𝑛θ =   𝑠𝑒𝑐²θ-1 𝑠𝑒𝑐θ =   1+𝑡𝑎𝑛²θ (𝑠𝑒𝑐θ - 𝑡𝑎𝑛θ)(𝑠𝑒𝑐θ + 𝑡𝑎𝑛θ)=1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ =1𝑠𝑒𝑐θ+𝑡𝑎𝑛θ 𝑠𝑒𝑐θ+𝑡𝑎𝑛θ = 1𝑠𝑒𝑐θ-𝑡𝑎𝑛θ
    www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π 1+𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ    ∀ θ ∈ ℝ -{𝑛π|𝑛∈ℤ}Corollaries:—————— 𝑐𝑜𝑠𝑒𝑐²θ - 𝑐𝑜𝑡²θ = 1𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ - 1𝑐𝑜𝑡θ =  𝑐𝑜𝑠𝑒𝑐²θ-1 𝑐𝑜𝑠𝑒𝑐θ =  1+𝑐𝑜𝑡²θ (𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ)(𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ)=1𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐+𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ-𝑐𝑜𝑡θ www.faastop.com الله π 1+𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ    ∀ θ ∈ ℝ -{𝑛π|𝑛∈ℤ}Corollaries:—————— 1+𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ    ∀ θ ∈ ℝ -{𝑛π|𝑛∈ℤ}Corollaries:—————— 𝑐𝑜𝑠𝑒𝑐²θ - 𝑐𝑜𝑡²θ = 1𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ - 1𝑐𝑜𝑡θ =  𝑐𝑜𝑠𝑒𝑐²θ-1 𝑐𝑜𝑠𝑒𝑐θ =  1+𝑐𝑜𝑡²θ (𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ)(𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ)=1𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐+𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ-𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐²θ - 𝑐𝑜𝑡²θ = 11+𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ    ∀ θ ∈ ℝ -{𝑛π|𝑛∈ℤ}Corollaries:—————— 𝑐𝑜𝑠𝑒𝑐²θ - 𝑐𝑜𝑡²θ = 1𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ - 1𝑐𝑜𝑡θ =  𝑐𝑜𝑠𝑒𝑐²θ-1 𝑐𝑜𝑠𝑒𝑐θ =  1+𝑐𝑜𝑡²θ (𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ)(𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ)=1𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐+𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ-𝑐𝑜𝑡θ 𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ - 11+𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ    ∀ θ ∈ ℝ -{𝑛π|𝑛∈ℤ}Corollaries:—————— 𝑐𝑜𝑠𝑒𝑐²θ - 𝑐𝑜𝑡²θ = 1𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ - 1𝑐𝑜𝑡θ =  𝑐𝑜𝑠𝑒𝑐²θ-1 𝑐𝑜𝑠𝑒𝑐θ =  1+𝑐𝑜𝑡²θ (𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ)(𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ)=1𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐+𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ-𝑐𝑜𝑡θ 𝑐𝑜𝑡θ =  𝑐𝑜𝑠𝑒𝑐²θ-1 1+𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ    ∀ θ ∈ ℝ -{𝑛π|𝑛∈ℤ}Corollaries:—————— 𝑐𝑜𝑠𝑒𝑐²θ - 𝑐𝑜𝑡²θ = 1𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ - 1𝑐𝑜𝑡θ =  𝑐𝑜𝑠𝑒𝑐²θ-1 𝑐𝑜𝑠𝑒𝑐θ =  1+𝑐𝑜𝑡²θ (𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ)(𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ)=1𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐+𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ-𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐θ =  1+𝑐𝑜𝑡²θ 1+𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ    ∀ θ ∈ ℝ -{𝑛π|𝑛∈ℤ}Corollaries:—————— 𝑐𝑜𝑠𝑒𝑐²θ - 𝑐𝑜𝑡²θ = 1𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ - 1𝑐𝑜𝑡θ =  𝑐𝑜𝑠𝑒𝑐²θ-1 𝑐𝑜𝑠𝑒𝑐θ =  1+𝑐𝑜𝑡²θ (𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ)(𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ)=1𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐+𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ-𝑐𝑜𝑡θ (𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ)(𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ)=11+𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ    ∀ θ ∈ ℝ -{𝑛π|𝑛∈ℤ}Corollaries:—————— 𝑐𝑜𝑠𝑒𝑐²θ - 𝑐𝑜𝑡²θ = 1𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ - 1𝑐𝑜𝑡θ =  𝑐𝑜𝑠𝑒𝑐²θ-1 𝑐𝑜𝑠𝑒𝑐θ =  1+𝑐𝑜𝑡²θ (𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ)(𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ)=1𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐+𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ-𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ 1+𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ    ∀ θ ∈ ℝ -{𝑛π|𝑛∈ℤ}Corollaries:—————— 𝑐𝑜𝑠𝑒𝑐²θ - 𝑐𝑜𝑡²θ = 1𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ - 1𝑐𝑜𝑡θ =  𝑐𝑜𝑠𝑒𝑐²θ-1 𝑐𝑜𝑠𝑒𝑐θ =  1+𝑐𝑜𝑡²θ (𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ)(𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ)=1𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐+𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ-𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐+𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ-𝑐𝑜𝑡θ 1+𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ    ∀ θ ∈ ℝ -{𝑛π|𝑛∈ℤ}Corollaries:—————— 𝑐𝑜𝑠𝑒𝑐²θ - 𝑐𝑜𝑡²θ = 1𝑐𝑜𝑡²θ = 𝑐𝑜𝑠𝑒𝑐²θ - 1𝑐𝑜𝑡θ =  𝑐𝑜𝑠𝑒𝑐²θ-1 𝑐𝑜𝑠𝑒𝑐θ =  1+𝑐𝑜𝑡²θ (𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ)(𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ)=1𝑐𝑜𝑠𝑒𝑐-𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ+𝑐𝑜𝑡θ 𝑐𝑜𝑠𝑒𝑐+𝑐𝑜𝑡θ =1𝑐𝑜𝑠𝑒𝑐θ-𝑐𝑜𝑡θ
    Even/Odd Identities
    𝑠𝑖𝑛(-θ) = - 𝑠𝑖𝑛(θ) www.faastop.com الله π 𝑠𝑖𝑛(-θ) = - 𝑠𝑖𝑛(θ)𝑠𝑖𝑛(-θ) = - 𝑠𝑖𝑛(θ)
    𝑐𝑜𝑠(-θ) = 𝑐𝑜𝑠(θ) www.faastop.com الله π 𝑐𝑜𝑠(-θ) = 𝑐𝑜𝑠(θ)𝑐𝑜𝑠(-θ) = 𝑐𝑜𝑠(θ)
    𝑡𝑎𝑛(-θ) = -𝑡𝑎𝑛(θ) www.faastop.com الله π 𝑡𝑎𝑛(-θ) = -𝑡𝑎𝑛(θ)𝑡𝑎𝑛(-θ) = -𝑡𝑎𝑛(θ)
    𝑐𝑜𝑡(-θ) = -𝑐𝑜𝑡(θ) www.faastop.com الله π 𝑐𝑜𝑡(-θ) = -𝑐𝑜𝑡(θ)𝑐𝑜𝑡(-θ) = -𝑐𝑜𝑡(θ)
    𝑐𝑜𝑠𝑒𝑐(-θ) = -𝑐𝑜𝑠𝑒𝑐(θ) www.faastop.com الله π 𝑐𝑜𝑠𝑒𝑐(-θ) = -𝑐𝑜𝑠𝑒𝑐(θ)𝑐𝑜𝑠𝑒𝑐(-θ) = -𝑐𝑜𝑠𝑒𝑐(θ)
    𝑠𝑒𝑐(-θ) = 𝑠𝑒𝑐(θ) www.faastop.com الله π 𝑠𝑒𝑐(-θ) = 𝑠𝑒𝑐(θ)𝑠𝑒𝑐(-θ) = 𝑠𝑒𝑐(θ)
    Periodic Identities
    𝑠𝑖𝑛(θ + 2nπ) = 𝑠𝑖𝑛θwww.faastop.comاللهπ𝑠𝑖𝑛(θ + 2nπ) = 𝑠𝑖𝑛θ𝑠𝑖𝑛(θ + 2nπ) = 𝑠𝑖𝑛θ
    𝑐𝑜𝑠(θ + 2nπ) = 𝑐𝑜𝑠θwww.faastop.comاللهπ𝑐𝑜𝑠(θ + 2nπ) = 𝑐𝑜𝑠θ𝑐𝑜𝑠(θ + 2nπ) = 𝑐𝑜𝑠θ
    𝑡𝑎𝑛(θ + nπ) = 𝑡𝑎𝑛θwww.faastop.comاللهπ𝑡𝑎𝑛(θ + nπ) = 𝑡𝑎𝑛θ𝑡𝑎𝑛(θ + nπ) = 𝑡𝑎𝑛θ
    𝑐𝑜𝑡(θ + nπ) = 𝑐𝑜𝑡θwww.faastop.comاللهπ 𝑐𝑜𝑡(θ + nπ) = 𝑐𝑜𝑡θ 𝑐𝑜𝑡(θ + nπ) = 𝑐𝑜𝑡θ
    𝑐𝑜𝑠𝑒𝑐(θ + 2nπ) = 𝑐𝑜𝑠𝑒𝑐θwww.faastop.comاللهπ 𝑐𝑜𝑠𝑒𝑐(θ + 2nπ) = 𝑐𝑜𝑠𝑒𝑐θ 𝑐𝑜𝑠𝑒𝑐(θ + 2nπ) = 𝑐𝑜𝑠𝑒𝑐θ
    𝑠𝑒𝑐(θ + 2nπ) = 𝑠𝑒𝑐θwww.faastop.comاللهπ 𝑠𝑒𝑐(θ + 2nπ) = 𝑠𝑒𝑐θ 𝑠𝑒𝑐(θ + 2nπ) = 𝑠𝑒𝑐θ
    Trigonometric Ratios Of Compound Angles
    𝑠𝑖𝑛(A-B)=𝑠𝑖𝑛A𝑐𝑜𝑠B-𝑐𝑜𝑠A𝑠𝑖𝑛B www.faastop.comاللهπ𝑠𝑖𝑛(A-B)=𝑠𝑖𝑛A𝑐𝑜𝑠B-𝑐𝑜𝑠A𝑠𝑖𝑛B 𝑠𝑖𝑛(A-B)=𝑠𝑖𝑛A𝑐𝑜𝑠B-𝑐𝑜𝑠A𝑠𝑖𝑛B
    𝑠𝑖𝑛(A+B)=𝑠𝑖𝑛A𝑐𝑜𝑠B+𝑐𝑜𝑠A𝑠𝑖𝑛Bwww.faastop.comاللهπ𝑠𝑖𝑛(A+B)=𝑠𝑖𝑛A𝑐𝑜𝑠B+𝑐𝑜𝑠A𝑠𝑖𝑛B𝑠𝑖𝑛(A+B)=𝑠𝑖𝑛A𝑐𝑜𝑠B+𝑐𝑜𝑠A𝑠𝑖𝑛B
    𝑐𝑜𝑠(A-B)=𝑐𝑜𝑠A𝑐𝑜𝑠B+𝑠𝑖𝑛A𝑠𝑖𝑛B www.faastop.comاللهπ𝑐𝑜𝑠(A-B)=𝑐𝑜𝑠A𝑐𝑜𝑠B+𝑠𝑖𝑛A𝑠𝑖𝑛B 𝑐𝑜𝑠(A-B)=𝑐𝑜𝑠A𝑐𝑜𝑠B+𝑠𝑖𝑛A𝑠𝑖𝑛B
    𝑐𝑜𝑠(A+B)=𝑐𝑜𝑠A𝑐𝑜𝑠B-𝑠𝑖𝑛A𝑠𝑖𝑛B www.faastop.comاللهπ𝑐𝑜𝑠(A+B)=𝑐𝑜𝑠A𝑐𝑜𝑠B-𝑠𝑖𝑛A𝑠𝑖𝑛B 𝑐𝑜𝑠(A+B)=𝑐𝑜𝑠A𝑐𝑜𝑠B-𝑠𝑖𝑛A𝑠𝑖𝑛B
    𝑡𝑎𝑛(A+B) = 𝑡𝑎𝑛A+𝑡𝑎𝑛B1-𝑡𝑎𝑛A𝑡𝑎𝑛B www.faastop.comاللهπ𝑡𝑎𝑛(A+B) = 𝑡𝑎𝑛A+𝑡𝑎𝑛B1-𝑡𝑎𝑛A𝑡𝑎𝑛B 𝑡𝑎𝑛(A+B) = 𝑡𝑎𝑛A+𝑡𝑎𝑛B1-𝑡𝑎𝑛A𝑡𝑎𝑛B
    𝑡𝑎𝑛(A-B) = 𝑡𝑎𝑛A-𝑡𝑎𝑛B1+𝑡𝑎𝑛A𝑡𝑎𝑛B www.faastop.comاللهπ𝑡𝑎𝑛(A-B) = 𝑡𝑎𝑛A-𝑡𝑎𝑛B1+𝑡𝑎𝑛A𝑡𝑎𝑛B 𝑡𝑎𝑛(A-B) = 𝑡𝑎𝑛A-𝑡𝑎𝑛B1+𝑡𝑎𝑛A𝑡𝑎𝑛B
    𝑐𝑜𝑡(A+B) = 𝑐𝑜𝑡A𝑐𝑜𝑡B-1𝑐𝑜𝑡A+𝑐𝑜𝑡B www.faastop.comاللهπ𝑐𝑜𝑡(A+B) = 𝑐𝑜𝑡A𝑐𝑜𝑡B-1𝑐𝑜𝑡A+𝑐𝑜𝑡B 𝑐𝑜𝑡(A+B) = 𝑐𝑜𝑡A𝑐𝑜𝑡B-1𝑐𝑜𝑡A+𝑐𝑜𝑡B
    𝑐𝑜𝑡(A-B) =𝑐𝑜𝑡A𝑐𝑜𝑡B-1𝑐𝑜𝑡B-𝑐𝑜𝑡A www.faastop.comاللهπ𝑐𝑜𝑡(A-B) =𝑐𝑜𝑡A𝑐𝑜𝑡B-1𝑐𝑜𝑡B-𝑐𝑜𝑡A 𝑐𝑜𝑡(A-B) =𝑐𝑜𝑡A𝑐𝑜𝑡B-1𝑐𝑜𝑡B-𝑐𝑜𝑡A
    𝑠𝑖𝑛(A+B)𝑠𝑖𝑛(A-B)=𝑠𝑖𝑛²A-𝑠𝑖𝑛²B www.faastop.comاللهπ𝑠𝑖𝑛(A+B)𝑠𝑖𝑛(A-B)=𝑠𝑖𝑛²A-𝑠𝑖𝑛²B 𝑠𝑖𝑛(A+B)𝑠𝑖𝑛(A-B)=𝑠𝑖𝑛²A-𝑠𝑖𝑛²B
    𝑠𝑖𝑛(A+B)𝑠𝑖𝑛(A-B)=𝑐𝑜𝑠²B-𝑐𝑜𝑠²A www.faastop.comاللهπ𝑠𝑖𝑛(A+B)𝑠𝑖𝑛(A-B)=𝑐𝑜𝑠²B-𝑐𝑜𝑠²A 𝑠𝑖𝑛(A+B)𝑠𝑖𝑛(A-B)=𝑐𝑜𝑠²B-𝑐𝑜𝑠²A
    𝑐𝑜𝑠(A+B)𝑐𝑜𝑠(A-B)=𝑐𝑜𝑠²A-𝑠𝑖𝑛²B www.faastop.comاللهπ𝑐𝑜𝑠(A+B)𝑐𝑜𝑠(A-B)=𝑐𝑜𝑠²A-𝑠𝑖𝑛²B 𝑐𝑜𝑠(A+B)𝑐𝑜𝑠(A-B)=𝑐𝑜𝑠²A-𝑠𝑖𝑛²B
    𝑐𝑜𝑠(A+B)𝑐𝑜𝑠(A-B)=𝑐𝑜𝑠²B-𝑠𝑖𝑛²A www.faastop.comاللهπ𝑐𝑜𝑠(A+B)𝑐𝑜𝑠(A-B)=𝑐𝑜𝑠²B-𝑠𝑖𝑛²A 𝑐𝑜𝑠(A+B)𝑐𝑜𝑠(A-B)=𝑐𝑜𝑠²B-𝑠𝑖𝑛²A
    𝑠𝑖𝑛(A+B+C) = 𝑠𝑖𝑛A𝑐𝑜𝑠B𝑐𝑜𝑠C+𝑐𝑜𝑠A𝑠𝑖𝑛B𝑐𝑜𝑠C+𝑐𝑜𝑠A𝑐𝑜𝑠B𝑠𝑖𝑛C-𝑠𝑖𝑛A𝑠𝑖𝑛B𝑠𝑖𝑛C www.faastop.comاللهπ𝑠𝑖𝑛(A+B+C) = 𝑠𝑖𝑛A𝑐𝑜𝑠B𝑐𝑜𝑠C+𝑐𝑜𝑠A𝑠𝑖𝑛B𝑐𝑜𝑠C+𝑐𝑜𝑠A𝑐𝑜𝑠B𝑠𝑖𝑛C-𝑠𝑖𝑛A𝑠𝑖𝑛B𝑠𝑖𝑛C 𝑠𝑖𝑛(A+B+C) = 𝑠𝑖𝑛A𝑐𝑜𝑠B𝑐𝑜𝑠C+𝑐𝑜𝑠A𝑠𝑖𝑛B𝑐𝑜𝑠C+𝑐𝑜𝑠A𝑐𝑜𝑠B𝑠𝑖𝑛C-𝑠𝑖𝑛A𝑠𝑖𝑛B𝑠𝑖𝑛C
    𝑐𝑜𝑠(A+B+C)= 𝑐𝑜𝑠A𝑐𝑜𝑠B𝑐𝑜𝑠C-𝑐𝑜𝑠A𝑠𝑖𝑛B𝑠𝑖𝑛C-𝑠𝑖𝑛A𝑐𝑜𝑠B𝑠𝑖𝑛C-𝑠𝑖𝑛A𝑠𝑖𝑛B𝑠𝑖𝑛C www.faastop.comاللهπ𝑐𝑜𝑠(A+B+C)= 𝑐𝑜𝑠A𝑐𝑜𝑠B𝑐𝑜𝑠C-𝑐𝑜𝑠A𝑠𝑖𝑛B𝑠𝑖𝑛C-𝑠𝑖𝑛A𝑐𝑜𝑠B𝑠𝑖𝑛C-𝑠𝑖𝑛A𝑠𝑖𝑛B𝑠𝑖𝑛C 𝑐𝑜𝑠(A+B+C)= 𝑐𝑜𝑠A𝑐𝑜𝑠B𝑐𝑜𝑠C-𝑐𝑜𝑠A𝑠𝑖𝑛B𝑠𝑖𝑛C-𝑠𝑖𝑛A𝑐𝑜𝑠B𝑠𝑖𝑛C-𝑠𝑖𝑛A𝑠𝑖𝑛B𝑠𝑖𝑛C
    𝑡𝑎𝑛(A+B+C) = 𝑡𝑎𝑛A+𝑡𝑎𝑛B+𝑡𝑎𝑛C-𝑡𝑎𝑛A𝑡𝑎𝑛B𝑡𝑎𝑛C1-𝑡𝑎𝑛A𝑡𝑎𝑛B-𝑡𝑎𝑛B𝑡𝑎𝑛C-𝑡𝑎𝑛C𝑡𝑎𝑛A www.faastop.comاللهπ𝑡𝑎𝑛(A+B+C) = 𝑡𝑎𝑛A+𝑡𝑎𝑛B+𝑡𝑎𝑛C-𝑡𝑎𝑛A𝑡𝑎𝑛B𝑡𝑎𝑛C1-𝑡𝑎𝑛A𝑡𝑎𝑛B-𝑡𝑎𝑛B𝑡𝑎𝑛C-𝑡𝑎𝑛C𝑡𝑎𝑛A 𝑡𝑎𝑛(A+B+C) = 𝑡𝑎𝑛A+𝑡𝑎𝑛B+𝑡𝑎𝑛C-𝑡𝑎𝑛A𝑡𝑎𝑛B𝑡𝑎𝑛C1-𝑡𝑎𝑛A𝑡𝑎𝑛B-𝑡𝑎𝑛B𝑡𝑎𝑛C-𝑡𝑎𝑛C𝑡𝑎𝑛A
    Double Angle Formulas
    www.faastop.com الله π 𝑠𝑖𝑛2A=2𝑠𝑖𝑛A𝑐𝑜𝑠A Corollaries:—————— 𝑠𝑖𝑛A = 2𝑠𝑖𝑛(   ——A2 ).𝑐𝑜𝑠(   ——A2 )www.faastop.com الله π 𝑠𝑖𝑛2A=2𝑠𝑖𝑛A𝑐𝑜𝑠A Corollaries:—————— 𝑠𝑖𝑛2A=2𝑠𝑖𝑛A𝑐𝑜𝑠A Corollaries:—————— 𝑠𝑖𝑛A = 2𝑠𝑖𝑛(   ——A2 ).𝑐𝑜𝑠(   ——A2 )𝑠𝑖𝑛A = 2𝑠𝑖𝑛(   ——A2 ).𝑐𝑜𝑠(   ——A2 )𝑠𝑖𝑛2A=2𝑠𝑖𝑛A𝑐𝑜𝑠A Corollaries:—————— 𝑠𝑖𝑛A = 2𝑠𝑖𝑛(   ——A2 ).𝑐𝑜𝑠(   ——A2 )
    www.faastop.com الله π 𝑠𝑖𝑛2A =2𝑡𝑎𝑛A1+𝑡𝑎𝑛²A Corollaries:—————— 𝑠𝑖𝑛A =2𝑡𝑎𝑛(A/2)1+𝑡𝑎𝑛²(A/2) www.faastop.com الله π 𝑠𝑖𝑛2A =2𝑡𝑎𝑛A1+𝑡𝑎𝑛²A Corollaries:—————— 𝑠𝑖𝑛2A =2𝑡𝑎𝑛A1+𝑡𝑎𝑛²A Corollaries:—————— 𝑠𝑖𝑛A =2𝑡𝑎𝑛(A/2)1+𝑡𝑎𝑛²(A/2) 𝑠𝑖𝑛A =2𝑡𝑎𝑛(A/2)1+𝑡𝑎𝑛²(A/2) 𝑠𝑖𝑛2A =2𝑡𝑎𝑛A1+𝑡𝑎𝑛²A Corollaries:—————— 𝑠𝑖𝑛A =2𝑡𝑎𝑛(A/2)1+𝑡𝑎𝑛²(A/2)
    www.faastop.com الله π 𝑐𝑜𝑠2A=𝑐𝑜𝑠²A-𝑠𝑖𝑛²A Corollaries:——————𝑐𝑜𝑠A=𝑐𝑜𝑠²(   ——A2 )-𝑠𝑖𝑛²(   ——A2 )www.faastop.com الله π 𝑐𝑜𝑠2A=𝑐𝑜𝑠²A-𝑠𝑖𝑛²A Corollaries:——————𝑐𝑜𝑠2A=𝑐𝑜𝑠²A-𝑠𝑖𝑛²A Corollaries:——————𝑐𝑜𝑠A=𝑐𝑜𝑠²(   ——A2 )-𝑠𝑖𝑛²(   ——A2 )𝑐𝑜𝑠A=𝑐𝑜𝑠²(   ——A2 )-𝑠𝑖𝑛²(   ——A2 )𝑐𝑜𝑠2A=𝑐𝑜𝑠²A-𝑠𝑖𝑛²A Corollaries:——————𝑐𝑜𝑠A=𝑐𝑜𝑠²(   ——A2 )-𝑠𝑖𝑛²(   ——A2 )
    www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π 𝑐𝑜𝑠2A=2𝑐𝑜𝑠²A-1 Corollaries:——————𝑐𝑜𝑠²A =1+𝑐𝑜𝑠2A2 𝑐𝑜𝑠A = 2𝑐𝑜𝑠²(   ——A2 )-1𝑐𝑜𝑠²(A/2) = 1-𝑐𝑜𝑠A2 𝑐𝑜𝑠(A/2) =+-1+𝑐𝑜𝑠A2 www.faastop.com الله π 𝑐𝑜𝑠2A=2𝑐𝑜𝑠²A-1 Corollaries:——————𝑐𝑜𝑠2A=2𝑐𝑜𝑠²A-1 Corollaries:——————𝑐𝑜𝑠²A =1+𝑐𝑜𝑠2A2 𝑐𝑜𝑠A = 2𝑐𝑜𝑠²(   ——A2 )-1𝑐𝑜𝑠²(A/2) = 1-𝑐𝑜𝑠A2 𝑐𝑜𝑠(A/2) =+-1+𝑐𝑜𝑠A2 𝑐𝑜𝑠²A =1+𝑐𝑜𝑠2A2 𝑐𝑜𝑠2A=2𝑐𝑜𝑠²A-1 Corollaries:——————𝑐𝑜𝑠²A =1+𝑐𝑜𝑠2A2 𝑐𝑜𝑠A = 2𝑐𝑜𝑠²(   ——A2 )-1𝑐𝑜𝑠²(A/2) = 1-𝑐𝑜𝑠A2 𝑐𝑜𝑠(A/2) =+-1+𝑐𝑜𝑠A2 𝑐𝑜𝑠A = 2𝑐𝑜𝑠²(   ——A2 )-1𝑐𝑜𝑠2A=2𝑐𝑜𝑠²A-1 Corollaries:——————𝑐𝑜𝑠²A =1+𝑐𝑜𝑠2A2 𝑐𝑜𝑠A = 2𝑐𝑜𝑠²(   ——A2 )-1𝑐𝑜𝑠²(A/2) = 1-𝑐𝑜𝑠A2 𝑐𝑜𝑠(A/2) =+-1+𝑐𝑜𝑠A2 𝑐𝑜𝑠²(A/2) = 1-𝑐𝑜𝑠A2 𝑐𝑜𝑠2A=2𝑐𝑜𝑠²A-1 Corollaries:——————𝑐𝑜𝑠²A =1+𝑐𝑜𝑠2A2 𝑐𝑜𝑠A = 2𝑐𝑜𝑠²(   ——A2 )-1𝑐𝑜𝑠²(A/2) = 1-𝑐𝑜𝑠A2 𝑐𝑜𝑠(A/2) =+-1+𝑐𝑜𝑠A2 𝑐𝑜𝑠(A/2) =+-1+𝑐𝑜𝑠A2 𝑐𝑜𝑠2A=2𝑐𝑜𝑠²A-1 Corollaries:——————𝑐𝑜𝑠²A =1+𝑐𝑜𝑠2A2 𝑐𝑜𝑠A = 2𝑐𝑜𝑠²(   ——A2 )-1𝑐𝑜𝑠²(A/2) = 1-𝑐𝑜𝑠A2 𝑐𝑜𝑠(A/2) =+-1+𝑐𝑜𝑠A2
    www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π www.faastop.com الله π 𝑐𝑜𝑠2A=1-2𝑠𝑖𝑛²A Corollaries:——————𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2 𝑠𝑖𝑛A =+-1-𝑐𝑜𝑠2A2 𝑐𝑜𝑠A=1-2𝑠𝑖𝑛² ——A2𝑠𝑖𝑛²(A/2) =1-𝑐𝑜𝑠A2 𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2 www.faastop.com الله π 𝑐𝑜𝑠2A=1-2𝑠𝑖𝑛²A Corollaries:——————𝑐𝑜𝑠2A=1-2𝑠𝑖𝑛²A Corollaries:——————𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2 𝑠𝑖𝑛A =+-1-𝑐𝑜𝑠2A2 𝑐𝑜𝑠A=1-2𝑠𝑖𝑛² ——A2𝑠𝑖𝑛²(A/2) =1-𝑐𝑜𝑠A2 𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2 𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2 𝑐𝑜𝑠2A=1-2𝑠𝑖𝑛²A Corollaries:——————𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2 𝑠𝑖𝑛A =+-1-𝑐𝑜𝑠2A2 𝑐𝑜𝑠A=1-2𝑠𝑖𝑛² ——A2𝑠𝑖𝑛²(A/2) =1-𝑐𝑜𝑠A2 𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2 𝑠𝑖𝑛A =+-1-𝑐𝑜𝑠2A2 𝑐𝑜𝑠2A=1-2𝑠𝑖𝑛²A Corollaries:——————𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2 𝑠𝑖𝑛A =+-1-𝑐𝑜𝑠2A2 𝑐𝑜𝑠A=1-2𝑠𝑖𝑛² ——A2𝑠𝑖𝑛²(A/2) =1-𝑐𝑜𝑠A2 𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2 𝑐𝑜𝑠A=1-2𝑠𝑖𝑛² ——A2𝑐𝑜𝑠2A=1-2𝑠𝑖𝑛²A Corollaries:——————𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2 𝑠𝑖𝑛A =+-1-𝑐𝑜𝑠2A2 𝑐𝑜𝑠A=1-2𝑠𝑖𝑛² ——A2𝑠𝑖𝑛²(A/2) =1-𝑐𝑜𝑠A2 𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2 𝑠𝑖𝑛²(A/2) =1-𝑐𝑜𝑠A2 𝑐𝑜𝑠2A=1-2𝑠𝑖𝑛²A Corollaries:——————𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2 𝑠𝑖𝑛A =+-1-𝑐𝑜𝑠2A2 𝑐𝑜𝑠A=1-2𝑠𝑖𝑛² ——A2𝑠𝑖𝑛²(A/2) =1-𝑐𝑜𝑠A2 𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2 𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2 𝑐𝑜𝑠2A=1-2𝑠𝑖𝑛²A Corollaries:——————𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2 𝑠𝑖𝑛A =+-1-𝑐𝑜𝑠2A2 𝑐𝑜𝑠A=1-2𝑠𝑖𝑛² ——A2𝑠𝑖𝑛²(A/2) =1-𝑐𝑜𝑠A2 𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2
    www.faastop.com الله π 𝑐𝑜𝑠2A =1-𝑡𝑎𝑛²A1+𝑡𝑎𝑛²ACorollaries:——————𝑐𝑜𝑠A =1-𝑡𝑎𝑛²(A/2)1+𝑡𝑎𝑛²(A/2) www.faastop.com الله π 𝑐𝑜𝑠2A =1-𝑡𝑎𝑛²A1+𝑡𝑎𝑛²ACorollaries:——————𝑐𝑜𝑠2A =1-𝑡𝑎𝑛²A1+𝑡𝑎𝑛²ACorollaries:——————𝑐𝑜𝑠A =1-𝑡𝑎𝑛²(A/2)1+𝑡𝑎𝑛²(A/2) 𝑐𝑜𝑠A =1-𝑡𝑎𝑛²(A/2)1+𝑡𝑎𝑛²(A/2) 𝑐𝑜𝑠2A =1-𝑡𝑎𝑛²A1+𝑡𝑎𝑛²ACorollaries:——————𝑐𝑜𝑠A =1-𝑡𝑎𝑛²(A/2)1+𝑡𝑎𝑛²(A/2)
    www.faastop.com الله π 𝑡𝑎𝑛2A = 2𝑡𝑎𝑛A1-𝑡𝑎𝑛²A Corollaries:——————𝑡𝑎𝑛A =2𝑡𝑎𝑛(A/2)1-𝑡𝑎𝑛²(A/2) www.faastop.com الله π 𝑡𝑎𝑛2A = 2𝑡𝑎𝑛A1-𝑡𝑎𝑛²A Corollaries:——————𝑡𝑎𝑛2A = 2𝑡𝑎𝑛A1-𝑡𝑎𝑛²A Corollaries:——————𝑡𝑎𝑛A =2𝑡𝑎𝑛(A/2)1-𝑡𝑎𝑛²(A/2) 𝑡𝑎𝑛A =2𝑡𝑎𝑛(A/2)1-𝑡𝑎𝑛²(A/2) 𝑡𝑎𝑛2A = 2𝑡𝑎𝑛A1-𝑡𝑎𝑛²A Corollaries:——————𝑡𝑎𝑛A =2𝑡𝑎𝑛(A/2)1-𝑡𝑎𝑛²(A/2)
    www.faastop.com الله π www.faastop.com الله π 𝑐𝑜𝑡2A = 𝑐𝑜𝑡²A-12𝑐𝑜𝑡A Corollaries:—————— 𝑐𝑜𝑡A = 𝑐𝑜𝑡²(A/2)-12𝑐𝑜𝑡(A/2) 2𝑐𝑜𝑡A = 𝑐𝑜𝑡 ( ——A2 ) - 𝑡𝑎𝑛 ( ——A2 ) www.faastop.com الله π 𝑐𝑜𝑡2A = 𝑐𝑜𝑡²A-12𝑐𝑜𝑡A Corollaries:—————— 𝑐𝑜𝑡2A = 𝑐𝑜𝑡²A-12𝑐𝑜𝑡A Corollaries:—————— 𝑐𝑜𝑡A = 𝑐𝑜𝑡²(A/2)-12𝑐𝑜𝑡(A/2) 2𝑐𝑜𝑡A = 𝑐𝑜𝑡 ( ——A2 ) - 𝑡𝑎𝑛 ( ——A2 )𝑐𝑜𝑡A = 𝑐𝑜𝑡²(A/2)-12𝑐𝑜𝑡(A/2) 𝑐𝑜𝑡2A = 𝑐𝑜𝑡²A-12𝑐𝑜𝑡A Corollaries:—————— 𝑐𝑜𝑡A = 𝑐𝑜𝑡²(A/2)-12𝑐𝑜𝑡(A/2) 2𝑐𝑜𝑡A = 𝑐𝑜𝑡 ( ——A2 ) - 𝑡𝑎𝑛 ( ——A2 )2𝑐𝑜𝑡A = 𝑐𝑜𝑡 ( ——A2 ) - 𝑡𝑎𝑛 ( ——A2 )𝑐𝑜𝑡2A = 𝑐𝑜𝑡²A-12𝑐𝑜𝑡A Corollaries:—————— 𝑐𝑜𝑡A = 𝑐𝑜𝑡²(A/2)-12𝑐𝑜𝑡(A/2) 2𝑐𝑜𝑡A = 𝑐𝑜𝑡 ( ——A2 ) - 𝑡𝑎𝑛 ( ——A2 )
    Multiple Angle Formulas
    𝑠𝑖𝑛3A = 3𝑠𝑖𝑛A-4𝑠𝑖𝑛³A www.faastop.comاللهπ𝑠𝑖𝑛3A = 3𝑠𝑖𝑛A-4𝑠𝑖𝑛³A 𝑠𝑖𝑛3A = 3𝑠𝑖𝑛A-4𝑠𝑖𝑛³A
    𝑐𝑜𝑠3A = 4𝑐𝑜𝑠³A-3𝑐𝑜𝑠A www.faastop.comاللهπ𝑐𝑜𝑠3A = 4𝑐𝑜𝑠³A-3𝑐𝑜𝑠A 𝑐𝑜𝑠3A = 4𝑐𝑜𝑠³A-3𝑐𝑜𝑠A
    𝑡𝑎𝑛3A = 3𝑡𝑎𝑛A-𝑡𝑎𝑛³A1-3𝑡𝑎𝑛²A www.faastop.comاللهπ𝑡𝑎𝑛3A = 3𝑡𝑎𝑛A-𝑡𝑎𝑛³A1-3𝑡𝑎𝑛²A 𝑡𝑎𝑛3A = 3𝑡𝑎𝑛A-𝑡𝑎𝑛³A1-3𝑡𝑎𝑛²A
    𝑐𝑜𝑡3A = 3𝑐𝑜𝑡A-𝑐𝑜𝑡³A1-3𝑐𝑜𝑡²A www.faastop.comاللهπ𝑐𝑜𝑡3A = 3𝑐𝑜𝑡A-𝑐𝑜𝑡³A1-3𝑐𝑜𝑡²A 𝑐𝑜𝑡3A = 3𝑐𝑜𝑡A-𝑐𝑜𝑡³A1-3𝑐𝑜𝑡²A
    Power Reduction Formulas
    𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2 www.faastop.comاللهπ𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2 𝑠𝑖𝑛²A =1-𝑐𝑜𝑠2A2
    𝑐𝑜𝑠²A =1+𝑐𝑜𝑠2A2 www.faastop.comاللهπ𝑐𝑜𝑠²A =1+𝑐𝑜𝑠2A2 𝑐𝑜𝑠²A =1+𝑐𝑜𝑠2A2
    𝑡𝑎𝑛²A =1-𝑐𝑜𝑠2A1+𝑐𝑜𝑠2A www.faastop.comاللهπ𝑡𝑎𝑛²A =1-𝑐𝑜𝑠2A1+𝑐𝑜𝑠2A 𝑡𝑎𝑛²A =1-𝑐𝑜𝑠2A1+𝑐𝑜𝑠2A
    𝑠𝑖𝑛³A = ——14 [3𝑠𝑖𝑛A-𝑠𝑖𝑛3A]www.faastop.comاللهπ𝑠𝑖𝑛³A = ——14 [3𝑠𝑖𝑛A-𝑠𝑖𝑛3A]𝑠𝑖𝑛³A = ——14 [3𝑠𝑖𝑛A-𝑠𝑖𝑛3A]
    𝑐𝑜𝑠³A= ——14 [𝑐𝑜𝑠3A+3𝑐𝑜𝑠A]www.faastop.comاللهπ𝑐𝑜𝑠³A= ——14 [𝑐𝑜𝑠3A+3𝑐𝑜𝑠A]𝑐𝑜𝑠³A= ——14 [𝑐𝑜𝑠3A+3𝑐𝑜𝑠A]
    Half Angle Formulas
    𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2 www.faastop.comاللهπ𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2 𝑠𝑖𝑛(A/2) =+-1-𝑐𝑜𝑠A2
    𝑐𝑜𝑠(A/2) =+-1+𝑐𝑜𝑠A2 www.faastop.comاللهπ𝑐𝑜𝑠(A/2) =+-1+𝑐𝑜𝑠A2 𝑐𝑜𝑠(A/2) =+-1+𝑐𝑜𝑠A2
    𝑡𝑎𝑛(A/2) =+-1-𝑐𝑜𝑠A1+𝑐𝑜𝑠A www.faastop.comاللهπ𝑡𝑎𝑛(A/2) =+-1-𝑐𝑜𝑠A1+𝑐𝑜𝑠A 𝑡𝑎𝑛(A/2) =+-1-𝑐𝑜𝑠A1+𝑐𝑜𝑠A
    Product To Sum Formulas
    2𝑠𝑖𝑛A𝑐𝑜𝑠B=𝑠𝑖𝑛(A+B)+𝑠𝑖𝑛(A-B) www.faastop.comاللهπ2𝑠𝑖𝑛A𝑐𝑜𝑠B=𝑠𝑖𝑛(A+B)+𝑠𝑖𝑛(A-B) 2𝑠𝑖𝑛A𝑐𝑜𝑠B=𝑠𝑖𝑛(A+B)+𝑠𝑖𝑛(A-B)
    2𝑐𝑜𝑠A𝑠𝑖𝑛B=𝑠𝑖𝑛(A+B)-𝑠𝑖𝑛(A-B) www.faastop.comاللهπ2𝑐𝑜𝑠A𝑠𝑖𝑛B=𝑠𝑖𝑛(A+B)-𝑠𝑖𝑛(A-B) 2𝑐𝑜𝑠A𝑠𝑖𝑛B=𝑠𝑖𝑛(A+B)-𝑠𝑖𝑛(A-B)
    2𝑐𝑜𝑠A𝑐𝑜𝑠B=𝑐𝑜𝑠(A+B)+𝑐𝑜𝑠(A-B) www.faastop.comاللهπ2𝑐𝑜𝑠A𝑐𝑜𝑠B=𝑐𝑜𝑠(A+B)+𝑐𝑜𝑠(A-B) 2𝑐𝑜𝑠A𝑐𝑜𝑠B=𝑐𝑜𝑠(A+B)+𝑐𝑜𝑠(A-B)
    2𝑠𝑖𝑛A𝑠𝑖𝑛B=𝑐𝑜𝑠(A-B)-𝑐𝑜𝑠(A+B) www.faastop.comاللهπ2𝑠𝑖𝑛A𝑠𝑖𝑛B=𝑐𝑜𝑠(A-B)-𝑐𝑜𝑠(A+B) 2𝑠𝑖𝑛A𝑠𝑖𝑛B=𝑐𝑜𝑠(A-B)-𝑐𝑜𝑠(A+B)
    Sum To Product Formulas
    𝑠𝑖𝑛C+𝑠𝑖𝑛D=2𝑠𝑖𝑛( ——C+D2  ) 𝑐𝑜𝑠( ——C-D2  )www.faastop.comاللهπ𝑠𝑖𝑛C+𝑠𝑖𝑛D=2𝑠𝑖𝑛( ——C+D2  ) 𝑐𝑜𝑠( ——C-D2  )𝑠𝑖𝑛C+𝑠𝑖𝑛D=2𝑠𝑖𝑛( ——C+D2  ) 𝑐𝑜𝑠( ——C-D2  )
    𝑠𝑖𝑛C-𝑠𝑖𝑛D=2𝑠𝑖𝑛( ——C-D2  ) 𝑐𝑜𝑠( ——C+D2  )www.faastop.comاللهπ𝑠𝑖𝑛C-𝑠𝑖𝑛D=2𝑠𝑖𝑛( ——C-D2  ) 𝑐𝑜𝑠( ——C+D2  )𝑠𝑖𝑛C-𝑠𝑖𝑛D=2𝑠𝑖𝑛( ——C-D2  ) 𝑐𝑜𝑠( ——C+D2  )
    𝑐𝑜𝑠C+𝑐𝑜𝑠D=2𝑐𝑜𝑠( ——C+D2  ) 𝑐𝑜𝑠( ——C-D2  )www.faastop.comاللهπ𝑐𝑜𝑠C+𝑐𝑜𝑠D=2𝑐𝑜𝑠( ——C+D2  ) 𝑐𝑜𝑠( ——C-D2  )𝑐𝑜𝑠C+𝑐𝑜𝑠D=2𝑐𝑜𝑠( ——C+D2  ) 𝑐𝑜𝑠( ——C-D2  )
    𝑐𝑜𝑠D-𝑐𝑜𝑠C=2𝑠𝑖𝑛( ——C+D2  ) 𝑠𝑖𝑛( ——C-D2  )www.faastop.comاللهπ𝑐𝑜𝑠D-𝑐𝑜𝑠C=2𝑠𝑖𝑛( ——C+D2  ) 𝑠𝑖𝑛( ——C-D2  )𝑐𝑜𝑠D-𝑐𝑜𝑠C=2𝑠𝑖𝑛( ——C+D2  ) 𝑠𝑖𝑛( ——C-D2  )

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