Question

Find the number of solutions of the equation $\cos \left({\cos }^{-1}x\right)=cosec\left(cose{c}^{-1}x\right)$

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C 2

$\cos \left({\cos }^{-1}x\right)=x$ for $xϵ[-1,1]$
$cosec\left(cose{c}^{-1}x\right)=x$ for $cϵ(-\infty ,-1]\cup [1,\infty )$
$\Rightarrow$ $\cos \left({\cos }^{-1}x\right)=cosec\left(cose{c}^{-1}x\right)$ for $x=\pm 1$ only.
Hence, there are two roots only.