CUET · MATHS · PYQ PAPER 2023
If \(x\) is in the 1 st Quadrant, then the value of \(\tan ^{-1}\left(\frac{\sqrt{1+\cos x}+\sqrt{1-\cos x}}{\sqrt{1+\cos x}-\sqrt{1-\cos x}}\right)\) is :
- A \(\frac{\pi}{4}-\frac{x}{2}\)
- B \(\frac{\pi}{4}+2 x\)
- C \(\frac{\pi}{4}+\frac{x}{2}\)
- D \(\frac{\pi}{4}-2 x\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{4}+\frac{x}{2}\)
Step-by-step Solution
Detailed explanation
\(\sqrt{1+\cos x}=\sqrt{2\cos^2\left(\frac{x}{2}\right)}=\sqrt{2}\cos\left(\frac{x}{2}\right)\) \(\sqrt{1-\cos x}=\sqrt{2\sin^2\left(\frac{x}{2}\right)}=\sqrt{2}\sin\left(\frac{x}{2}\right)\)…
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