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The value of \cos 5 x-\cos 3 x is

Option: 1

4 \sin ^2 x


Option: 2

2 \sin ^2 x


Option: 3

-4 \sin ^2 x


Option: 4

-2 \sin ^2 x


Answers (1)

best_answer

Given that,

\cos 5 x-\cos 3 x

Using the third SOP identity formula,

\cos A \cos B=-2 \sin \left(\frac{A+B}{2}\right)\cos \left(\frac{A-B}{2}\right)
\cos 5 x-\cos 3 x=-2 \sin \frac{(5 x+3 x)}{2} \cos \frac{(5 x-3 x)}{2}
\cos 5 x-\cos 3 x=-2 \sin 4 x \cos 2 x
\cos 5 x-\cos 3 x=-4 \sin ^2 x

 

Posted by

Divya Prakash Singh

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