45. cot²x cot² x cos²x
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- Verifying a Trigonometric Identity In Exercises 65 and 66, use the double-angle formulas to verify the identity algebraically and use a graphing utility to confirm your result graphically. sin4x=8cos3xsinx4cosxsinxUsing a Calculator In Exercises 43-48, use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.) cos(2.8)Simplifying a Trigonometric Expression In Exercises 7-16, use the fundamental trigonometric identities to simplify the expression. (There is more than one correct form of each answer.) tan1cos2
- Trigonometric Substitution In Exercises 59–62,use the trigonometric substitution to write the algebraicequation as a trigonometric equation of θ, where−π2 < θ < π2. Then find sin θ and cos θ.59. √2 = √4 − x2, x = 2 sin θ60. 2√2 = √16 − 4x2, x = 2 cos θ61. 3 = √36 − x2, x = 6 sin θ62. 5√3 = √100 − x2, x = 10 cos θProof Use the trigonometric identitycos2 x + sin2 x = 1 to prove that (Hint: Beginby multiplying the numerator and denominator by cos x + 1.)Verification of Trigonometric Identities