Question

Number of real roots of the equation $\left|\begin{array}{cc}\sin x& x\\ 1& 1\end{array}\right|\left|\begin{array}{cc}\cos x& x\\ x& 1\end{array}\right|=0$, is

Answer 1

Answer: 3

We have $\left|\begin{array}{cc}\sin x& x\\ 1& 1\end{array}\right|\left|\begin{array}{cc}\cos x& x\\ x& 1\end{array}\right|=0$

$\Rightarrow (\sin x-x)\left(\cos x-x^2\right)=0$
$\therefore$ Either $\sin x=x$ or $\cos x=x^2$
Hence, number of real roots are $3$ .