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Question: \(\sin\left\{ \tan^{- 1}\left( \frac{1 - x^{2}}{2x} \right) + \cos^{- 1}\left( \frac{1 - x^{2}}{1 + ...

sin⁡{tan⁡−1(1−x22x)+cos⁡−1(1−x21+x2)}\sin\left\{ \tan^{- 1}\left( \frac{1 - x^{2}}{2x} \right) + \cos^{- 1}\left( \frac{1 - x^{2}}{1 + x^{2}} \right) \right\} is equal to

A

0

B

1

C

2\sqrt{2}

D

12\frac{1}{\sqrt{2}}

Answer

1

Explanation

Solution

sin⁡{(π2−2tan⁡−1x)+2tan⁡−1x}\sin\left\{ \left( \frac{\pi}{2} - 2\tan^{- 1}x \right) + 2\tan^{- 1}x \right\} = sin⁡π2\sin\frac{\pi}{2} = 1