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Question: tan \(\left\lbrack \cos^{- 1}\frac{4}{5} + \tan^{- 1}\frac{2}{3} \right\rbrack\)=...

tan [cos⁡−145+tan⁡−123]\left\lbrack \cos^{- 1}\frac{4}{5} + \tan^{- 1}\frac{2}{3} \right\rbrack=

A

617\frac{6}{17}

B

176\frac{17}{6}

C

716\frac{7}{16}

D

167\frac{16}{7}

Answer

176\frac{17}{6}

Explanation

Solution

tan [tan⁡−1(1−16/25)4/5+tan⁡−12/3\tan^{- 1}\frac{\sqrt{(1 - 16/25)}}{4/5} + \tan^{- 1}2/3

= tan . tan–117/6 = 17/6