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Jee Main 2025 — Medium JEE math MCQ

If $\sin x + \sin^2 x = 1, x \in \left(0, \frac{\pi}{2}\right)$, then $(\cos^{12} x + x \tan^{12} x) + 3 (\cos^{10} x + \tan^{10} x + \cos^8 x + \tan^8 x) + (\cos^6 x + \tan^6 x)$ is equal to
  1. A. 4
  2. B. $\frac{4}{3}$
  3. C. 3
  4. D. 2

Solution

The correct option is **D**. (D. 2)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
If sin⁡x+sin⁡2x=1,x∈(0,π2)\sin x + \sin^2 x = 1, x \in \left(0, \frac{\pi}{2}\right), then (cos⁡12x+xtan⁡12x)+3(cos⁡10x+tan⁡10x+cos⁡8x+tan⁡8x)+(cos⁡6x+tan⁡6x)(\cos^{12} x + x \tan^{12} x) + 3 (\cos^{10} x + \tan^{10} x + \cos^8 x + \tan^8 x) + (\cos^6 x + \tan^6 x) is equal to
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