Solveeit Logo
Login

Question

Question: \(\frac{\text{cosech}x}{\sqrt{\text{cosec}\text{h}^{2}x + 1}}\) equals....

cosechxcosech2x+1\frac{\text{cosech}x}{\sqrt{\text{cosec}\text{h}^{2}x + 1}} equals.

A

tanh⁡x\tanh x

B

coth⁡x\coth x

C

sec⁡⥂hx\sec ⥂ hx

D

cos⁡hx{\cos h}x

Answer

sec⁡⥂hx\sec ⥂ hx

Explanation

Solution

cosechxcosech2x+1=cosechxcot⁡h2x=cosech xcot⁡hx\frac{\text{cosech}x}{\sqrt{\text{cosec}\text{h}^{2}x + 1}} = \frac{\text{cosech}x}{\sqrt{{\cot h}^{2}x}} = \frac{\text{cosech }x}{{\cot h}x}

=1sin⁡hxcos⁡hxsin⁡hx=sech x= \frac{\frac{1}{{\sin h}x}}{\frac{{\cos h}x}{{\sin h}x}} = \text{sech }x.