Inverse Circular Functions Ques 7
- Prove that $\cos \tan ^{-1}\left[\sin \left(\cot ^{-1} x\right)\right]=\sqrt{\frac{x^{2}+1}{x^{2}+2}}$.
(2002, 5M)
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Answer:
Correct Answer: 7.3
Solution:
- LHS $=\cos \tan ^{-1}\left[\sin \left(\cot ^{-1} x\right)\right]$
$ \begin{aligned} & =\cos \tan ^{-1} [\sin (\sin ^{-1} \frac{1}{\sqrt{1+x^{2}}})] \\ & =\cos (\tan ^{-1} \frac{1}{\sqrt{1+x^{2}}})=\sqrt{\frac{x^{2}+1}{x^{2}+2}}=\text { RHS } \end{aligned} $
BETA
