Question

The value of $\frac{cotx-\tan x}{cot2x}$ is

• A. $1$
• B. $2$
• C. $-1$
• D. $4$

Answer 1

The correct option is B

$2$

Explanation for the correct option:

Find the required value.

$\frac{cotx-\tan x}{cot2x}=\frac{{\displaystyle \frac{\cos x}{\sin x}}-{\displaystyle \frac{\sin x}{\cos x}}}{{\displaystyle \frac{\cos 2x}{\sin 2x}}}$

$$\begin{gathered} =\frac{\left({\cos }^{2}x-{\sin }^{2}x\right)\sin 2x}{\sin x\cos x\cos 2x} \\ =\frac{2\cos 2x\sin 2x}{2\sin x\cos x\cos 2x}\left[\because {\cos }^{2}x-{\sin }^{2}x=\cos 2x\right] \\ =\frac{2\sin 2x}{\sin 2x}\left[\because 2\sin x\cos x=\sin 2x\right] \\ =2 \end{gathered}$$

Hence, option (B) is the correct answer.