Question

Number of solutions for $2^{\sin |x|}=4^{|\cos x|}$ in $[-\pi ,\pi ]$ is equal to

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is B $4$

$y=4^{|\cos x|}$ and $y=2^{\sin |x|}$
$\therefore 2|\cos x|=\sin |x|$
The total number of solutions for the given equation is equal to the number of points of intersection of curves $y=2|\cos x|$ and $y=\sin |x|$.

Clearly, the two curves intersect at four points. So, there are four solutions of the given equation.

Hence, option 'B' is correct.