Question

The number of solution of $\sin |x|=|\cos x|$ in $[-3\pi ,3\pi ]$ is

Answer 1

The number of solution of $\sin |x|=|\cos x|$ is equal to the number of points where garphs of $\sin |x|$ and $|\cos x|$ intersect each other.

As the graph of $\sin |x|$ and $|\cos x|$ is symmetric abour $y-$ axis, so

The number of solution in $[-3\pi ,3\pi ]$ is double of the number of solutions in $[0,3\pi ]$
Now, drawing the graphs, we get


There are $4$ points of intersection in $[0,3\pi ]$

Hence, the number of solution is $8$.