Question

$\frac{d\left[\log \right(\tan x\left)\right]}{dx}=$

• A. $2sec2x$
• B. $2\cos ec2x$
• C. $sec2x$
• D. $\cos ec2x$

Answer 1

The correct option is B

$2\cos ec2x$

Explanation for correct option:

Let, $\mathrm{y}=\log \left(\mathrm{tanx}\right)$

Then,

$\begin{array}{rcl}& \Rightarrow & \frac{dy}{dx}=\left(\frac{1}{\tan x}\right)\times se{c}^{2}x\\ & =& \frac{\cos x}{\sin x}\times \frac{1}{{\cos }^{2}x}\\ & =& \frac{2}{2\sin x\cos x}\\ & =& \frac{2}{\sin 2x}\\ & =& 2\cos ec2x\end{array}$

Hence, correct option is $\mathbf{\left(}\mathbf{B}\mathbf{\right)}$.