# How do you use trigonometric substitution to write the algebraic expression sqrt(x^2-4) as a trigonometric function of theta where 0<theta<pi/2 and x=2sectheta?

Jul 29, 2017

#### Answer:

$2 \tan \theta$

#### Explanation:

•color(white)(x)tan^2x=sec^2x-1

$\text{substitute "x=2sectheta" into } \sqrt{{x}^{2} - 4}$

$\Rightarrow \sqrt{4 {\sec}^{2} \theta - 4}$

=sqrt(4(sec^2theta-1)

$= \sqrt{4 {\tan}^{2} \theta}$

$= 2 \tan \theta \to 0 < \theta < \frac{\pi}{2}$