720 CHAPTER 7 Trigonometric Identities and Equations 7.4 Exercises CONCEPT PREVIEW Match each expression in Column I with its value in Column II. I 1. 2 cos2 15° - 1 2. 2 tan 15° 1 - tan2 15° 3. 2 sin 22.5° cos 22.5° 4. cos2 p 6 - sin2 p 6 5. 4 sin p 3 cos p 3 6. 2 tan p 3 1 - tan2 p 3 II A. 1 2 B. 22 2 C. 23 2 D. - 23 E. 23 3 F. 23 CONCEPT PREVIEW Determine whether the positive or negative square root should be selected. 7. sin 195° = {B1 - cos 390° 2 8. cos 58° = {B1 + cos 116° 2 9. tan 225° = {B1 - cos 450° 1 + cos 450° 10. sin1-10°2 = {B1 - cos1-20°2 2 Verifying an Identity EXAMPLE 12 Verifying an Identity Verify that the following equation is an identity. asin x 2 + cos x 2b 2 = 1 + sin x SOLUTION We work on the more complicated left side. asin x 2 + cos x 2b 2 = sin2 x 2 + 2 sin x 2 cos x 2 + cos2 x 2 1x + y22 = x2 + 2 xy + y2 = 1 + 2 sin x 2 cos x 2 sin2 x 2 + cos 2 x 2 = 1 = 1 + sin 2 a x 2b 2 sin x 2 cos x 2 = sin 2 A x 2B = 1 + sin x Multiply. S Now Try Exercise 93. Remember the middle term when squaring a binomial. (b) Use the identity tan A 2 = 1 - cos A sin A with A = 5a. 1 - cos 5a sin 5a = tan 5a 2 S Now Try Exercises 71 and 73.
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