[ ^ - 1 1 3 + ^ - 1 1 2 ] = - Vidyadip

MCQ

$\cos \left[ {{{\tan }^{ - 1}}\frac{1}{3} + {{\tan }^{ - 1}}\frac{1}{2}} \right] = $

✓
$\frac{1}{{\sqrt 2 }}$
B
$\frac{{\sqrt 3 }}{2}$
C
$\frac{1}{2}$
D
$\frac{\pi }{4}$

✓

Answer

Correct option: A.

$\frac{1}{{\sqrt 2 }}$

a
(a) $\cos \,\left[ {{{\tan }^{ - 1}}\frac{1}{3} + {{\tan }^{ - 1}}\frac{1}{2}} \right] = \cos \,\left[ {{{\tan }^{ - 1}}\left( {\frac{{\frac{1}{3} + \frac{1}{2}}}{{1 - \frac{1}{3} \times \frac{1}{2}}}} \right)} \right]$

$ = \cos \,\{ {\tan ^{ - 1}}(1)\} = \cos \frac{\pi }{4} = \frac{1}{{\sqrt 2 }}$.

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