https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/trigonometry-identity-review-fun 2021-05-05T14:53:24Z Trig angle addition identities Sal reviews 6 related trigonometric angle addition identities: sin(a+b), sin(a-c), cos(a+b), cos(a-b), cos(2a), and sin(2a). Sal Khan video https://cdn.kastatic.org/googleusercontent/q779WlSevH6c0FCkG6uJcgjnP-3oXG6igoQNkUMmaUC_iYs2ef5ZtpHgGVMziteKMOmz7gjlpqZzF16rq8z2hxo Trig angle addition identities Sal reviews 6 related trigonometric angle addition identities: sin(a+b), sin(a-c), cos(a+b), cos(a-b), cos(2a), and sin(2a). https://cdn.kastatic.org/ka-youtube-converted/a70-dYvDJZY.mp4/a70-dYvDJZY.mp4 667 Angle addition identities https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/cosine-addition-identity-example 2021-05-05T14:53:16Z Using the cosine angle addition identity Sal evaluates the cosine of the sum of 60° and another angle whose right triangle is given. To do this, he must use the cosine angle addition formula. Sal Khan video https://cdn.kastatic.org/googleusercontent/OirHRBIT_x63S6CU99h-fPyl2X_hDf7HZAM9tO9PaiIgSfaay7XSpcxQW-xYIn2jLljKXyz0qnd0vzmSZ1J7HWFVGA Using the cosine angle addition identity Sal evaluates the cosine of the sum of 60° and another angle whose right triangle is given. To do this, he must use the cosine angle addition formula. https://cdn.kastatic.org/ka-youtube-converted/h0SNEO25vIw.mp4/h0SNEO25vIw.mp4 314 Angle addition identities https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/double-angle-formula-for-cosine-example-c 2021-05-05T14:53:17Z Using the cosine double-angle identity The cosine double angle formula tells us that cos(2θ) is always equal to cos²θ-sin²θ. For example, cos(60) is equal to cos²(30)-sin²(30). We can use this identity to rewrite expressions or solve problems. See some examples in this video. Sal Khan video https://cdn.kastatic.org/googleusercontent/152bMm2bPz9qxWTKf3kD6x5ejlJKR-tLzP7uUkfHeN7OOT9OJRqTPVW19HlJJNGXMZ8DK5MLDrNHrPU91DCpPMs Using the cosine double-angle identity The cosine double angle formula tells us that cos(2θ) is always equal to cos²θ-sin²θ. For example, cos(60) is equal to cos²(30)-sin²(30). We can use this identity to rewrite expressions or solve problems. See some examples in this video. https://cdn.kastatic.org/ka-youtube-converted/D_smr0GBPvA.mp4/D_smr0GBPvA.mp4 208 Angle addition identities https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/e/trig_addition_identities 2026-06-09T17:40:46.212160686Z Use the trig angle addition identities Find the trig values of sums of angles whose individual trig values are known. Mark Wittels exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/proof-angle-addition-sine 2021-05-05T14:53:16Z Proof of the sine angle addition identity Sal proves the identity sin(x+y) = sin(x)*cos(y) + cos(x)*sin(y). Sal Khan video https://cdn.kastatic.org/googleusercontent/egZR3z6x8IGAPeU5EAdzsvyL4RnjWigy9B_OnXbOh9W2mw3jSIKSig9uvNCMNyx0M0UpGJrLARgaoIfUhhq7fZI Proof of the sine angle addition identity Sal proves the identity sin(x+y) = sin(x)*cos(y) + cos(x)*sin(y). https://cdn.kastatic.org/ka-youtube-converted/R0EQg9vgbQw.mp4/R0EQg9vgbQw.mp4 506 Angle addition identities https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/proof-angle-addition-cosine 2021-05-05T14:53:19Z Proof of the cosine angle addition identity Sal proves the identity cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y). Sal Khan video https://cdn.kastatic.org/googleusercontent/FasP1nWHi_ADiQthXb5kLHxdJw2ww_abdrkLF2zuHo7X1r1TOAfd37BLg1JOjGdEEn4-K8Bde1hl2aYF_vZzn6Zb Proof of the cosine angle addition identity Sal proves the identity cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y). https://cdn.kastatic.org/ka-youtube-converted/0VBQnR2h8XM.mp4/0VBQnR2h8XM.mp4 362 Angle addition identities https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/proof-of-the-tangent-angle-sum-and-difference-identities 2022-10-07T00:22:18.752150461Z Proof of the tangent angle sum and difference identities Using the sine and cosine of the sum or difference of two angles, we can prove: tan(x+y)=(tan(x)+tan(y))/(1-tan(x)tan(y)) Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/cb68ce3e-f475-452f-abac-faf2ed53d3a7_1280_720_base.png Proof of the tangent angle sum and difference identities Using the sine and cosine of the sum or difference of two angles, we can prove: tan(x+y)=(tan(x)+tan(y))/(1-tan(x)tan(y)) https://cdn.kastatic.org/ka-youtube-converted/nUlElr4LXz8.mp4/nUlElr4LXz8.mp4 415 Angle addition identities https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:using-trig-id/a/trig-identity-reference 2024-10-28T20:22:05.023706061Z Trig identity reference Look up AND understand all your favorite trig identities article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:using-trig-id/a/trig-faq 2022-10-26T00:13:38.755031109Z Trigonometry: FAQ article