Question

$\frac{d}{dx}\cos h^{-1}(secx)=?$

• A. $\sec \mathrm{x}$
• B. $\tan x$
• C. $\sin x$
• D. $\mathrm{cosec}x$

Answer 1

The correct option is A

$\sec \mathrm{x}$

Finding the value:

We know that

$$\begin{gathered} \frac{d\left(\cos h^{-1}x\right)}{dx}=\frac{1}{\sqrt{x^2-1}} \\ \mathbf{} \end{gathered}$$

Let $y=\cos h^{-1}(secx)$

$$\begin{gathered} \frac{dy}{dx}=\left[\frac{1}{\sqrt{(se{c}^{2}x-1)}}\right](secx\tan x) \\ =\frac{(secx\tan x)}{\sqrt{{\tan }^{2}x}} \\ =\frac{(secx\tan x)}{\tan x} \\ \mathbf{} \end{gathered}$$

$\Rightarrow$ $\frac{\mathbf{dy}}{\mathbf{dx}}\mathbf{=}\mathit{s}\mathit{e}\mathit{c}\mathbf{}\mathit{x}$

Hence, option (A) is correct.