Question

evaluate
Cos(tan^-1 1/3+ tan^-1 1/2)​

Answer 1

Step-by-step explanation:

We have,

$\cos( \tan^{ - 1} ( \frac{1}{3} ) + \tan^{ - 1} ( \frac{1}{2} ) )$

$= \cos( \tan^{ - 1} ( \frac{ \frac{1}{3} + \frac{1}{2} }{1 - \frac{1}{6} } ) )$

$= \cos( \tan^{ - 1} ( \frac{ \frac{5}{6} }{ \frac{5}{6} } ) )$

$= \cos( \tan^{ - 1} ( 1 ) )$

$= \cos( \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} }$