1 + ^2 ( ^ - 1 x) = - Vidyadip

MCQ

$1 + {\cot ^2}({\sin ^{ - 1}}x) = $

A
$\frac{1}{{2x}}$
B
${x^2}$
✓
$\frac{1}{{{x^2}}}$
D
$\frac{2}{x}$

✓

Answer

Correct option: C.

$\frac{1}{{{x^2}}}$

c
(c) Let ${\sin ^{ - 1}}x = \theta \,\, \Rightarrow \,\,\sin \theta = x$

Now $1 + {\cot ^2}\theta = \cos e{c^2}\theta = \frac{1}{{{x^2}}}$

Hence $1 + {\cot ^2}\,({\sin ^{ - 1}}x) = \frac{1}{{{x^2}}}$.

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