706 CHAPTER 7 Trigonometric Identities and Equations Verifying an Identity EXAMPLE 7 Verifying an Identity Verify that the following equation is an identity. sin a p 6 + ub + cos a p 3 + ub = cos u SOLUTION Work on the left side, using the sine and cosine sum identities. sin a p 6 + ub + cos a p 3 + ub = asin p 6 cos u + cos p 6 sin ub + acos p 3 cos u - sin p 3 sin ub Sine sum identity; cosine sum identity = ¢ 1 2 cos u + 23 2 sin u≤ + ¢ 1 2 cos u - 23 2 sin u≤ sin p 6 = 1 2 ; cos p 6 = 23 2 ; cos p 3 = 1 2 ; sin p 3 = 23 2 = 1 2 cos u + 1 2 cos u Simplify. = cos u Add. The left side is identical to the right side, so the given equation is an identity. S Now Try Exercise 95. CONCEPT PREVIEW Match each expression in Column I with the correct expression in Column II to form an identity. I 7. sin1A + B2 8. sin1A - B2 9. tan1A + B2 10. tan1A - B2 II A. sin A cos B - cos A sin B B. tan A + tan B 1 - tan A tan B C. tan A - tan B 1 + tan A tan B D. sin A cos B + cos A sin B 7.3 Exercises CONCEPT PREVIEW Match each expression in Column I with the correct expression in Column II to form an identity. Choices may be used once, more than once, or not at all. I 1. cos1x + y2 = _____ 2. cos1x - y2 = _____ 3. cos Ap 2 - xB = _____ 4. sin Ap 2 - xB = _____ 5. cos Ax - p 2 B = _____ 6. sin Ax - p 2 B = _____ II A. cos x cos y + sin x sin y B. -cos x C. -sin x D. sin x E. cos x cos y - sin x sin y F. cos x
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