Exercises 20.2, page 546

  1. 1. 1665

  2. 3.

    sin 105 °  = sin 60 ° cos 45 °  + cos 60 °  sin 45 °  = 3222 + 1222 = 0.9659

  3. 5.

    cos 15 °  = cos(60 °  − 45 ° ) = cos 60 °  cos 45 °  + sin 60 °  sin 45 °  = (12)(122) + (123)(122) = 142 + 146 = 14(2 + 6) = 0.9659

  4. 7.  − 3365

  5. 9.  − 5665

  6. 11. sin 3x

  7. 13. cos 4x

  8. 15. cos x

  9. 17. tan x

  10. 19. 0

  11. 21. 1

  12. 23. 0

  13. 25.

    (sin x cos y  +  cos x sin y) (sin x cos y  –  cos x sin y) =  sin2 x cos2 y  –  cos 2 x sin2 y =  sin 2 x(1  –  sin2 y)  –  (1  –  sin2 x)sin2 y  =  sin2 x  –  sin2 yMathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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bcacaWG4bGaaeiiaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaa=bcacaWG5baabaGaeyypa0JaaeiiaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaabccacaWG4bGaaiikaiaaigdacaqGGaWdbiaacobipaGaaeiiaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaabccacaWG5bGaaiykaiaabccapeGaai4eG8aacaqGGaGaaiikaiaaigdacaqGGaWdbiaacobipaGaaeiiaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaabccacaWG4bGaaiykaiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaabccacaWG5bGaaeiiaiabg2da9iaabccaciGGZbGaaiyAaiaac6gadaahaaWcbeqaaiaaikdaaaGccaqGGaGaamiEaiaabccapeGaai4eG8aacaqGGaGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOGaaeiiaiaadMhaaaaa@AFA7@ ...

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