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