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MathsJEE Main 24 Jan 2026, Shift 1·Q10·MCQ·Moderate

Trigonometry · Half angle and compound angles

If cot⁡x=512\cot x = \dfrac{5}{12} for some x∈(π,3π2)x \in \left(\pi, \dfrac{3\pi}{2}\right), then sin⁡7x(cos⁡13x2+sin⁡13x2)+cos⁡7x(cos⁡13x2−sin⁡13x2)\sin7x\left(\cos\dfrac{13x}{2} + \sin\dfrac{13x}{2}\right) + \cos7x\left(\cos\dfrac{13x}{2} - \sin\dfrac{13x}{2}\right) is equal to
  1. (1)426\dfrac{4}{\sqrt{26}}
  2. (2)626\dfrac{6}{\sqrt{26}}
  3. (3)113\dfrac{1}{\sqrt{13}}
  4. (4)513\dfrac{5}{\sqrt{13}}

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