Question

Number of solution(s) of the equation $2{\cos }^2\theta -3\sqrt{2}\cos \theta +2=0$ in $(0,10)$ is

Answer 1

$2{\cos }^2\theta -3\sqrt{2}\cos \theta +2=0$
$\Rightarrow (2\cos \theta -\sqrt{2})(\cos \theta -\sqrt{2})=0$
$\Rightarrow \cos \theta =\frac{1}{\sqrt{2}}\text{or}\cos \theta =\sqrt{2}\text{(rejected)}$
$\Rightarrow \cos \theta =\frac{1}{\sqrt{2}}$
If $\theta \in (0,10),$ then $\theta =\{\frac{\pi }{4},\frac{7\pi }{4},\frac{9\pi }{4}\}$
$\therefore$ Number of solutions is $3.$