cos3θ−cos7θ=

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Q.

$\cos 3 θ - \cos 7 θ =$

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a

$- 2 \sin 5 θ \cdot \sin 2 θ$

b

$2 \cos 5 θ \cdot \cos 2 θ$

c

$2 \sin 5 θ \cdot \sin 2 θ$

d

$2 \sin 5 θ \cdot \cos 2 θ$

answer is D.

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Detailed Solution

$\cos 3 θ - \cos 7 θ$

$\cos C - \cos D = 2 \sin (\frac{C + D}{2}) \sin (\frac{D - C}{2})$

$= 2 \sin (\frac{3 θ + 7 θ}{2}) \sin (\frac{7 θ - 3 θ}{2})$

$= 2 \sin 5 θ \cdot \sin 2 θ$

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