Question

Which of the following given statements is/are not correct?

• A. $\frac{d}{dx}\left(\text{cosec}x\right)=\text{cosec}x.\cot x$
• B. $\frac{d}{dx}\left(\sec x\right)=\sec x.\tan x$
• C. $\frac{d}{dx}\left(3\cot x\right)=-3{\text{cosec}}^{2}x$
• D. $\frac{d}{dx}\left(2\tan x\right)=-2{\sec }^{2}x$

Answer 1

Answer: (A), (D)

$\frac{d}{dx}\left(\text{cosec}x\right)=\text{cosec}x.\cot x$
$\frac{d}{dx}\left(2\tan x\right)=-2{\sec }^{2}x$

We will see for all the options:

$A\left)\frac{d}{dx}\right(cosec\left(x\right))=-cosec(x).cot(x)$

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

$C\left)\frac{d}{dx}\right[3\times cot\left(x\right)]=-3\times co{sec}^2(x)$

$D\left)\frac{d}{dx}\right[2\times tan\left(x\right)]=2\times {sec}^2(x)$

Option A and D are correct.