Question

The number of solutions of the equation ${cos}^{-1}(1-x)+m{\cos }^{-1}x=\frac{n\pi }{2},wherem>0,n\le 0is$

• A. $0$
• B. $1$
• C. $2$
• D. None of these

Answer 1

The correct option is C $2$

Given,

${\cos }^{-1}(1-x)+m{\cos }^{-1}x=\frac{n\pi }{2}$

Let,

${\cos }^{-1}(1-x)+m{\cos }^{-1}x=0$

now,

$\Rightarrow {\cos }^{-1}(1-x)=0$

$1-x=\cos 0$

$1-x=1$

$x=0$

$\Rightarrow m{\cos }^{-1}x=0$

$x=\cos \left(\frac{0}{m}\right)$

$x=1$

$x=0,1$