Question

Suppose equation $f\left(x\right)-g\left(x\right)=0$ or $f\left(x\right)=g\left(x\right)=y$ say, then draw the graphs of $y=f\left(x\right)$ and $y=g\left(x\right)$. If graphs of $y=f\left(x\right)$ and $y=g\left(x\right)$ cuts at one, two, three, no points, then number of solutions are one, two, three,zero respectively. On the basis of above information, answer the following question.

Total number of solutions of

$\cos 2x=|\sin x|$, where $x\in (-\frac{\pi }{2},\pi )$ is:

• A. $5$
• B. $3$
• C. $4$
• D. $6$

Answer 1

The correct option is B $3$

From the graph we can see that

$y=\cos 2x$ and $y=|\sin x|$ meet at $3$ points from $[-\frac{\pi }{2},\pi ]$