Question

Number of values of $x$ satisfying the equation ${\cos }^{-1}(x^2-$ $5x+6)=2{\cot }^{-1}(1)$, is equal to

Answer 1

Answer: 2

Given, ${\cos }^{-1}\left(x^2-5x+6\right)=2{\cot }^{-1}1$
$\Rightarrow {\cos }^{-1}\left(x^2-5x+6\right)=2\times \frac{\pi }{4}=\frac{\pi }{2}$
$\Rightarrow x^2-5x+6=0$
$\Rightarrow (x-2)(x-3)=0$
$\therefore x=2,3$.
i.e. $2$ values