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
- A \(\frac{\pi}{4}+\frac{x}{2}\)
- B \(\frac{\pi}{4}-\frac{x}{2}\)
- C \(\frac{\pi}{2}+x\)
- D \(\frac{\pi}{4}+x\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{4}-\frac{x}{2}\)
Step-by-step Solution
Detailed explanation
\(\tan ^{-1}\left(\frac{\cos x}{1+\sin x}\right) = \tan ^{-1}\left(\frac{\cos ^{2} \frac{x}{2}-\sin ^{2} \frac{x}{2}}{\cos ^{2} \frac{x}{2}+\sin ^{2} \frac{x}{2}+2 \sin \frac{x}{2} \cos \frac{x}{2}}\right)\)…
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