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MathsJEE Main 23 Jan 2026, Shift 2·Q2·MCQ·Moderate

Trigonometry · Compound angle formulae

Let π2<θ<π\dfrac{\pi}{2} < \theta < \pi and cot⁡θ=−122\cot\theta = -\dfrac{1}{2\sqrt2}. Then the value of sin⁡(15θ2)(cos⁡8θ+sin⁡8θ)+cos⁡(15θ2)(cos⁡8θ−sin⁡8θ)\sin\left(\dfrac{15\theta}{2}\right)(\cos8\theta + \sin8\theta) + \cos\left(\dfrac{15\theta}{2}\right)(\cos8\theta - \sin8\theta) is equal to:
  1. (1)1−23\dfrac{1-\sqrt2}{\sqrt3}
  2. (2)−23-\dfrac{\sqrt2}{\sqrt3}
  3. (3)2−13\dfrac{\sqrt2-1}{\sqrt3}
  4. (4)23\dfrac{\sqrt2}{\sqrt3}
We corrected a printing error in the original paper

Source printed “(cos⁡8−sin⁡8θ)(\cos8 - \sin8\theta)” (the θ\theta of cos⁡8θ\cos8\theta missing).

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