Question

Number of solutions of the equation $\sin x=\cos x$ in the interval $[-2\pi ,2\pi ]$ is

• A. $3$
• B. $4$
• C. $5$
• D. $2$

Answer 1

The correct option is B $4$

Number of solutions $=$ Number of points of intersection of $y=\sin x$ and $y=\cos x$ in the given interval
From this graph we see that $y=\sin x$ and $y=\cos x$ intersect at $4$ points in the interval $[-2\pi ,2\pi ]$