Question

What is the value of [(cos 7a + cos 5a)÷(sin 7a – sin 5a)]?

Answer 1

HEYA !

$\frac{ \cos7a + \cos5a }{ \sin7a - \sin5a } \\ \\ = \frac{2 \cos \big( \frac{7 a+ 5a} {2} \big ) \cos \big( \frac{7a - 5a}{2} \big) }{2 \ \cos \big( \frac{7a + 5a}{2} \big) \sin \big( \frac{7a - 5a}{2} \big) } \\ \\ = \frac{ \cos \big( \frac{2a}{2} \big) }{ \sin \big( \frac{2a}{2} \big ) } = \frac{ \cos a }{ \sin a} \\ \\ = \cot a \: \: \: \: \: \: \: \mathbf{Ans.}$
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Formula used :

• cosx + cosy = 2cos(x+y / 2)cos(x-y / 2)

• sinx - siny = 2 cos(x+y / 2) sin(x-y / 2)

Answer 2

Helll friend

Good morning

Your answer is given in the attachment

I hope it will help you a lot

Thanks

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