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Chapter 7: Q. 17 (page 500)

express each sum or difference as a product of sines and/or cosines
$\sin 4 ϑ - \sin 2 ϑ$

Short Answer

Expert verified

$2 \cos (3 ϑ) \sin (ϑ)$

Step by step solution

01

Step 1. Given Information

$\sin 4 ϑ - \sin 2 ϑ$

02

Step 2. Solving using identity

We know that :

$\sin x - \sin y = 2 \cos (\frac{x + y}{2}) \sin (\frac{x - y}{2})$

Using it :

$\sin 4 ϑ - \sin 2 ϑ = 2 \cos (\frac{4 ϑ + 2 ϑ}{2}) \sin (\frac{4 ϑ - 2 ϑ}{2}) \sin 4 ϑ - \sin 2 ϑ = 2 \cos (3 ϑ) \sin (ϑ)$

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Most popular questions from this chapter

Graph $f (x) = \sin^{2} x = \frac{1 - \cos (2 x)}{2}$ for $0 \leq x \leq 2 π$ by hand using transformations.

Find the exact value of the expression:

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If $z = \tan \frac{α}{2}$ , show that localid="1646416257885" $\cos α = \frac{1 - z^{2}}{1 + z^{2}}$ .

Establish each identity.

$\frac{\sin^{3} θ + \cos^{3} θ}{1 - 2 \cos^{2} θ} = \frac{s e c θ - \sin θ}{\tan θ - 1}$

solve each equation on the interval

$0 \leq θ < 2 π$

$\sin θ + \cos θ = \sqrt{2}$

See all solutions

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