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MCQMediumJEE Main 2026 · 24 January, Shift 1Trigonometric Ratios & Identities

Mathematics Question from JEE Main 2026 · 24 January, Shift 1

If cot⁡x=512\cot x=\dfrac{5}{12} for some x∈(π,3π2)x\in(\pi,\tfrac{3\pi}{2}), then sin⁡7x(cos⁡13x2+sin⁡13x2)+cos⁡7x(cos⁡13x2−sin⁡13x2)\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

  • A

    113\dfrac{1}{\sqrt{13}}

  • B

    426\dfrac{4}{\sqrt{26}}

  • C

    513\dfrac{5}{\sqrt{13}}

  • D

    626\dfrac{6}{\sqrt{26}}

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