Question

$\frac{\cos echx}{\sqrt{(\cos ec{h}^{2}x+1)}}$ equals

• A. $\tan hx$
• B. $cothx$
• C. $sechx$
• D. $\cos hx$

Answer 1

The correct option is C

$sechx$

Explanation for the correct option:

Given, $\frac{\cos echx}{\sqrt{(\cos ec{h}^{2}x+1)}}$

Use the identity $\mathit{c}\mathit{o}\mathit{t}{\mathit{h}}^{\mathbf{2}}\mathit{x}\mathbf{}\mathbf{–}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{e}\mathit{c}{\mathit{h}}^{\mathbf{2}}\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}$,

$=\frac{\cos echx}{\sqrt{\left(cot{h}^{2}x\right)}}$

$=\frac{\cos echx}{cothx}$

$=\frac{\left({\displaystyle \frac{1}{\sin hx}}\right)}{\left({\displaystyle \frac{\cos hx}{\sin hx}}\right)}$

$=\frac{1}{\cos hx}$

$=\mathit{s}\mathit{e}\mathit{c}\mathit{h}\mathbf{}\mathit{x}$

Hence, Option ‘C’ is Correct.