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Jee Main 2025 — Medium JEE math MCQ

If \( \frac{\pi}{6} \leq x \leq \frac{3\pi}{4} \), then \( \cos^{-1}\left(\frac{12}{13}\cos x + \frac{5}{13}\sin x\right) \) is equal to
  1. A. \( x - \tan^{-1}\frac{4}{3} \) -
  2. B. \( x + \tan^{-1}\frac{4}{5} \) -
  3. C. \( x - \tan^{-1}\frac{5}{12} \) -
  4. D. \( x + \tan^{-1}\frac{5}{12} \)

Solution

The correct option is **C**. (C. \( x - \tan^{-1}\frac{5}{12} \) -)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
If π6≤x≤3π4 \frac{\pi}{6} \leq x \leq \frac{3\pi}{4} , then cos⁡−1(1213cos⁡x+513sin⁡x) \cos^{-1}\left(\frac{12}{13}\cos x + \frac{5}{13}\sin x\right) is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep