^ - 1 [ ( 2 , ^ - 1 3 4 ) , + , , ( 2 , ^ - 1 1 2 ) ] is - Vidyadip

MCQ

${\tan ^{ - 1}}\left[ {\cos \left( {2\,{{\tan }^{ - 1}}\frac{3}{4}} \right)\, + \,\sin \,\left( {2\,{{\cot }^{ - 1}}\frac{1}{2}} \right)} \right]$ is

A
not real
B
equal to $\frac{\pi }{4}$
✓
greater than $\frac{\pi }{4}$
D
less than $\frac{\pi }{4}$

✓

Answer

Correct option: C.

greater than $\frac{\pi }{4}$

c
$\tan ^{-1}\left[\cos \left(2 \tan ^{-1} \frac{3}{4}\right)+\sin \left(2 \cot ^{-1} \frac{1}{2}\right)\right]$

$=\tan ^{-1}\left(1+\frac{2}{25}\right)>\frac{\pi}{4}$

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