Match the given expression with an expression that has exactly the same value. Do not use a calculator. $\sin (54^{\circ})$ Choose the expression below that is equal to $\sin (54^{\circ})$ A. $-\sin (54^{\circ})$ B. $\cos (36^{\circ})$ C. $\cos (54^{\circ})$ D. $\sin (36^{\circ})$
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We need to use trigonometric identities. Step 2: Recall the complementary angle identity for sine and cosine. The complementary angle identity states that for any angle $\theta$, $\sin(\theta) = \cos(90^{\circ} - \theta)$. Step 3: Apply the identity to the given Show more…
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Use one or more of the six sum and difference identities to find the exact value of the expression sin(45° + 60°). Apply the sum and difference identities. Choose the correct answer below. A. cos 60° cos 60° + sin 45° sin 45° B. sin 45° cos 45° + cos 60° sin 60° C. sin 45° cos 60° - cos 45° sin 60° D. cos 45° cos 45° - sin 60° sin 60° E. cos 45° cos 60° + sin 45° sin 60° F. (tan 60° - tan 45°) / (1 - tan 45° tan 60°) G. cos 45° cos 45° + sin 60° sin 60° H. sin 45° cos 45° - cos 60° sin 60° I. cos 60° cos 60° - sin 45° sin 45° J. sin 60° cos 60° - sin 45° cos 45° K. sin 45° cos 60° + cos 45° sin 60° L. (tan 45° - tan 60°) / (1 + tan 45° tan 60°) M. (tan 45° + tan 60°) / (1 - tan 45° tan 60°) N. cos 45° cos 60° - sin 45° sin 60° Find the exact value of the expression. sin(45° + 60°) = (sqrt(2) + sqrt(6)) / 4 (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize the denominator.)
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