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Chapter 7: Q. 10 (page 500)

Express the product $\sin (3 θ) \sin (5 θ)$ as a sum containing only sines or only cosines.

Short Answer

Expert verified

$\sin (3 θ) \sin (5 θ) = \frac{\cos (2 θ) - \cos (8 θ)}{2}$

Step by step solution

01

Step 1. Given expression

$\sin (3 θ) \sin (5 θ)$

02

Step 2. Rewriting the expression

$2 \sin A \sin B = \cos (A - B) - \cos (A + B) S o, \sin (3 θ) \sin (5 θ) = \frac{\cos (2 θ) - \cos (8 θ)}{2}$

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Most popular questions from this chapter

Establish each identity.

$\frac{{(2 \cos^{2} θ - 1)}^{2}}{\cos^{4} θ - \sin^{4} θ} = 1 - 2 \sin^{2} θ$

In Problems 9–36, find the exact value of each expression.

$\cos^{- 1} (\sin \frac{5 π}{4})$

Rewrite over a common denominator:

$\frac{\sin (θ) + \cos (θ)}{\cos (θ)} + \frac{\sin (θ) + \cos (θ)}{\sin (θ)}$

Express the product $\cos (4 θ) \cos (2 θ)$ as a sum containing only sines or only cosines.

solve each equation on the interval $0 \leq θ < 2 π$

$\sin θ - \sqrt{3} \cos θ = 1$

See all solutions

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