Question

Number of solution(s) of the equation ${\cos }^{2}x+\cos x={\sin }^{2}x$ where $x\in [0,\pi ]$ is

Answer 1

${\cos }^{2}x+\cos x={\sin }^{2}x$
$\Rightarrow {\cos }^{2}x+\cos x=1-{\cos }^{2}x$
$\Rightarrow 2{\cos }^{2}x+\cos x-1=0$
$\Rightarrow (2\cos x-1)(\cos x+1)=0$
$\Rightarrow \cos x=\frac{1}{2}$ or $\cos x=-1$
​​​​​​​$\therefore x=\frac{\pi }{3},\pi$