Question

The number of solutions of the equation $\left(1-\cos \left(2x\right)\right)\left(\cos \left(2x\right)+\cot \left(2x\right)\right)=0,0\le x\le 2\pi$ is

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is D

$0$

Explanation for correct option

Given, $\left(1-\cos \left(2x\right)\right)\left(\cos \left(2x\right)+\cot \left(2x\right)\right)=0$

$\therefore \cos \left(2x\right)=1$

That means $x=0,\pi ,2\pi$

$\cot \left(x\right)$ is not defined for $x=0,\pi ,2\pi$

Therefore, there will be no solution for the given equation

Hence, the correct option is $\left(\mathrm{D}\right)$