# If sec x=3 and tan x=2sqrt 2, what are the values of sin x and cos ^2 x?

Sep 25, 2016

$\sin x = 2 \frac{\sqrt{2}}{3} , \mathmr{and} , {\cos}^{2} x = \frac{1}{9}$

#### Explanation:

We have, $\tan x = \sin \frac{x}{\cos} x = \sin x \cdot \sec x$

Given that, $\sec x = 3 , \tan x = 2 \sqrt{2}$

Sub.ing, we get, $2 \sqrt{2} = 3 \sin x \Rightarrow \sin x = 2 \frac{\sqrt{2}}{3}$

${\cos}^{2} x = \frac{1}{\sec} ^ 2 x = \frac{1}{3} ^ 2 = \frac{1}{9.}$