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CUET · MATHS · PYQ PAPER 2025

The simplified form of \(\tan ^{-1}\left(\frac{\cos x}{1+\sin x}\right),-\frac{\pi}{2}< x <\frac{\pi}{2}\) is

  1. A \(\frac{\pi}{4}+\frac{x}{2}\)
  2. B \(\frac{\pi}{4}-\frac{x}{2}\)
  3. C \(\frac{\pi}{2}+x\)
  4. D \(\frac{\pi}{4}+x\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\pi}{4}-\frac{x}{2}\)

Step-by-step Solution

Detailed explanation

\(\tan ^{-1}\left(\frac{\cos x}{1+\sin x}\right) = \tan ^{-1}\left(\frac{\cos ^{2} \frac{x}{2}-\sin ^{2} \frac{x}{2}}{\cos ^{2} \frac{x}{2}+\sin ^{2} \frac{x}{2}+2 \sin \frac{x}{2} \cos \frac{x}{2}}\right)\)…