If cot x = 5 12 for some x (, 3 2 ) , then sin 7 x ( cos 13 x 2 + sin 13 x 2 ) + cos 7 x ( cos 13 x 2 - sin 13 x 2 ) is equal to [2026]

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Solution

Q.
If $\cot x = \frac{5}{12}$ for some $x \in (π, \frac{3 π}{2}),$ then $\sin 7 x (\cos \frac{13 x}{2} + \sin \frac{13 x}{2}) + \cos 7 x (\cos \frac{13 x}{2} - \sin \frac{13 x}{2})$ is equal to [2026]

1 $\frac{1}{\sqrt{13}}$

2 $\frac{6}{\sqrt{26}}$

3 $\frac{5}{\sqrt{13}}$

4 $\frac{4}{\sqrt{26}}$

Ans.
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