If r=1∑13{sin(4π+(r−1)6π)sin(4π+6rπ)1}=a3+b,a,b∈Z, then a2+b2 is equal to :
Held on 28 Jan 2025 · Verified 6 Jul 2026.
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If $\cot x=\frac{5}{12}$ for some $x \in\left(\pi, \frac{3 \pi}{2}\right)$, then $\sin 7 x\left(\cos \frac{13 x}{2}+\sin \frac{13 x}{2}\right)+\cos 7 x\left(\cos \frac{13 x}{2}-\sin \frac{13 x}{2}\right)$ is equal to
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