Q

# Write the following functions in the simplest form: 6.

Write the following functions in the simplest form:

6. $\tan^{-1} \frac{1}{\sqrt{x^2 -1}},\;\; |x| > 1$

Views

Given that $\tan^{-1} \frac{1}{\sqrt{x^2 -1}},\;\; |x| > 1$

Take $x =cosec\ \Theta$  or  $\Theta = cosec ^{-1}x$

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

$=tan^{-1} \frac{1}{\sqrt{cosec^2 \Theta -1}}$

$=tan^{-1}(\frac{1}{\cot \Theta})$

$=tan^{-1}(\tan \Theta)$  =  $\Theta$

$cosec^{-1}x$

$=\frac{\pi}{2}- \sec^{-1}x$        $[\because cosec^{-1}x + \sec^{-1}x = \frac{\pi}{2}]$

Exams
Articles
Questions