Mathematics · 2026
JEE Main · 24 January 2026, Shift 1 · Q12
If cot x=5/12 for some x ∈(π, (3 π)/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
If $\displaystyle \cot x=\frac{5}{12}$ for some $\displaystyle x \in\left(\pi, \frac{3 \pi}{2}\right)$, then $\displaystyle \sin 7 x\left(\cos \frac{13 x}{2}+\sin \frac{13 x}{2}\right)+\cos 7 x\left(\cos \frac{13 x}{2}-\sin \frac{13 x}{2}\right)$ is equal to
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle \frac{1}{\sqrt{13}}$
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JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.