SECTION 7.5 Sum and Difference Formulas 521 Skill Building In Problems 13–24, find the exact value of each expression. 13. cos ° 165 14. sin ° 105 15. tan ° 15 16. tan ° 195 17. π sin 5 12 18. π sin 12 19. π cos 7 12 20. π tan 7 12 21. π sin 17 12 22. π tan 19 12 23. π ( ) − sec 12 24. π ( ) − cot 5 12 In Problems 25–34, find the exact value of each expression. 25. ° ° + ° ° sin20 cos10 cos20 sin10 26. ° ° − ° ° sin20 cos80 cos20 sin80 27. ° ° − ° ° cos70 cos20 sin 70 sin20 28. ° ° + ° ° cos40 cos10 sin40 sin10 29. ° + ° − ° ° tan20 tan25 1 tan20 tan25 30. ° − ° + ° ° tan40 tan10 1 tan40 tan10 31. π π π π − sin 12 cos 7 12 cos 12 sin 7 12 32. π π π π − cos 5 12 cos 7 12 sin 5 12 sin 7 12 33. π π π π + cos 12 cos 5 12 sin 5 12 sin 12 34. π π π π + sin 18 cos 5 18 cos 18 sin 5 18 In Problems 35–40, find the exact value of each of the following under the given conditions: (a) α β ( ) + sin (b) α β ( ) + cos (c) α β ( ) − sin (d) α β ( ) − tan 35. α α π β π β = < < = − < < sin 3 5 , 0 2 ; cos 2 5 5 , 2 0 36. α α π β π β = < < = − − < < cos 5 5 , 0 2 ; sin 4 5 , 2 0 37. α π α π β β π = − < < = < < tan 4 3 , 2 ; cos 1 2 , 0 2 38. α π α π β π β π = < < = − < < tan 5 12 , 3 2 ; sin 1 2 , 3 2 39. α π α π β π β π = − < <− = − < < sin 5 13 , 3 2 ; tan 3, 2 40. α π α β β π = − < < = < < cos 1 2 , 2 0; sin 1 3 , 0 2 41. If θ θ = sin 1 3 , in quadrant II, find the exact value of: (a) θ cos (b) θ π ( ) + sin 6 (c) θ π ( ) − cos 3 (d) θ π ( ) + tan 4 42. If θ θ = cos 1 4 , in quadrant IV, find the exact value of: (a) θ sin (b) θ π ( ) − sin 6 (c) θ π ( ) + cos 3 (d) θ π ( ) − tan 4 In Problems 43–48, use the figures to evaluate each function if ( ) = = f x x g x x sin, () cos, and ( ) = h x x tan . 43. α β + f( ) 44. α β + g( ) 45. α β − g( ) 46. α β − f( ) 47. α β ( ) + h 48. α β ( ) − h y x (x, 1) x2 1 y2 5 4 a y x ( , y) x2 1 y2 5 1 b 1 – 3 In Problems 49–74, establish each identity. 49. π θ θ ( ) + = sin 2 cos 50. π θ θ ( ) + = − cos 2 sin 51. π θ θ ( ) − = sin sin 52. π θ θ ( ) − = − cos cos 53. π θ θ ( ) + = − sin sin 54. π θ θ ( ) + = − cos cos 55. π θ θ ( ) − = − tan tan 56. π θ θ ( ) − = − tan 2 tan 57. π θ θ ( ) + = − sin 3 2 cos 58. π θ θ ( ) + = cos 3 2 sin 59. α β α β α β ( ) ( ) + + − = sin sin 2 sin cos
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