# How do you find the value of csc [arctan(x/sqrt2)]?

##### 1 Answer
Nov 11, 2016

$\csc \left[\arctan \left(\frac{x}{\sqrt{2}}\right)\right]$

$= \csc \left[a r c \cot \left(\frac{\sqrt{2}}{x}\right)\right]$

$= \csc \left[a r c \csc \sqrt{1 + {\left(\frac{\sqrt{2}}{x}\right)}^{2}}\right]$

$= \sqrt{1 + {\left(\frac{\sqrt{2}}{x}\right)}^{2}}$

$= \sqrt{1 + \frac{2}{x} ^ 2}$

$= \frac{\sqrt{{x}^{2} + 2}}{x}$