Write ^ -1 (1 x^ 2 -1 ), x>1 in the simplest form. - Vidyadip

MCQ

Write $\cot ^{-1}\left(\frac{1}{\sqrt{x^{2}-1}}\right), x>1$ in the simplest form.

✓
$\sec ^{-1} x$
B
$cosec ^{-1} x$
C
$tan ^{-1} x$
D
$cot ^{-1} x$

✓

Answer

Correct option: A.

$\sec ^{-1} x$

a
Let $x=\sec \theta,$ then $\sqrt{x^{2}-1}=\sqrt{\sec ^{2} \theta-1}=\tan \theta$

Therefore, $\cot ^{-1} \frac{1}{\sqrt{x^{2}-1}}=\cot ^{-1}(\cot \theta)$$=\theta=\sec ^{-1} x$

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