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Question

Question: \(2\tan^{- 1}\left( \frac{1}{\sqrt{2}} \right)\) is equal to....

2tan⁡−1(12)2\tan^{- 1}\left( \frac{1}{\sqrt{2}} \right) is equal to.

A

cosh⁡−1(13)\cosh^{- 1}\left( \frac{1}{3} \right)

B

cos⁡h−1(3){\cos h}^{- 1}(\sqrt{3})

C

cosh⁡−1(3)\cosh^{- 1}(3)

D

cos⁡h−1(2+12−1){\cos h}^{- 1}\left( \frac{\sqrt{2} + 1}{\sqrt{2} - 1} \right)

Answer

cosh⁡−1(3)\cosh^{- 1}(3)

Explanation

Solution

∵2tan⁡h−1x=cos⁡h−1(1+x21−x2)\because 2{\tan h}^{- 1}x = {\cos h}^{- 1}\left( \frac{1 + x^{2}}{1 - x^{2}} \right)

⇒ 2tan⁡h−1(1/2)=cos⁡h−1(1+1/21−1/2)=cos⁡h−1(3)2{\tan h}^{- 1}(1/\sqrt{2}) = {\cos h}^{- 1}\left( \frac{1 + 1/2}{1 - 1/2} \right) = {\cos h}^{- 1}(3).