^ - 1 ( 3 5 ) + ^ - 1 ( 1 7 ) = - Vidyadip

MCQ

${\sin ^{ - 1}}\left( {\frac{3}{5}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right) = $

✓
$\frac{\pi }{4}$
B
$\frac{\pi }{2}$
C
${\cos ^{ - 1}}\left( {\frac{4}{5}} \right)$
D
$\pi $

✓

Answer

Correct option: A.

$\frac{\pi }{4}$

a
(a) ${\sin ^{ - 1}}\frac{3}{5} + {\tan ^{ - 1}}\frac{1}{7} = {\tan ^{ - 1}}\frac{3}{4} + {\tan ^{ - 1}}\frac{1}{7}$

$ = {\tan ^{ - 1}}\left( {\frac{{(3/4) + (1/7)}}{{1 - (3/4) \times (1/7)}}} \right) $

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

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