MHT CET · Maths · Inverse Trigonometric Functions
If \(2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)\), then the value of \(x\) is
- A \(-\frac{\pi}{4}\)
- B \(0\)
- C \(\frac{\pi}{8}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\tan^{-1}\left(\frac{2 \cos x}{1-\cos^2 x}\right)=\tan^{-1}(2 \operatorname{cosec} x)\) \(\frac{2 \cos x}{\sin^2 x}=2 \operatorname{cosec} x\)
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