If $\cot x=\frac{5}{12}$ for some $x\in \left(\pi ,\frac{3\pi }{2}\right),$ then $\sin 7x\left(\cos \frac{13x}{2}+\sin \frac{13x}{2}\right)+$ $\cos 7x\left(\cos \frac{13x}{2}−\sin \frac{13x}{2}\right)$ is equal to

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If \(\cot x=\frac{5}{12}\) for some \(x\in \left(\pi ,\frac{3\pi }{2}\right),\) then \(\sin 7x\left(\cos \frac{13x}{2}+\…

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