^ - 1 x a^2 - x^2 = - Vidyadip

MCQ

${\tan ^{ - 1}}\frac{x}{{\sqrt {{a^2} - {x^2}} }} = $

A
$\frac{1}{a}{\sin ^{ - 1}}\left( {\frac{x}{a}} \right)$
B
$a{\sin ^{ - 1}}\left( {\frac{x}{a}} \right)$
✓
${\sin ^{ - 1}}\left( {\frac{x}{a}} \right)$
D
${\sin ^{ - 1}}\left( {\frac{a}{x}} \right)$

✓

Answer

Correct option: C.

${\sin ^{ - 1}}\left( {\frac{x}{a}} \right)$

c
(c) ${\tan ^{ - 1}}\frac{x}{{\sqrt {{a^2} - {x^2}} }} = {\tan ^{ - 1}}\,\left( {\frac{{a\,\sin \theta }}{{a\,\cos \theta }}} \right)$ ( Putting $x = a\,\sin \theta )$

$ = {\tan ^{ - 1}}(\tan \theta ) = \theta = {\sin ^{ - 1}}\left( {\frac{x}{a}} \right)$.

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