# How do you show that 1+tan^2 theta = sec ^2 theta?

Mar 3, 2018

Here is the answer:-

#### Explanation:

$1 + {\tan}^{2} \theta = {\sec}^{2} \theta$
$\tan \theta = \sin \frac{\theta}{\cos} \theta$ and
$\sec \theta = \frac{1}{\cos} \theta$

$1 + {\sin}^{2} \frac{\theta}{\cos} ^ 2 \theta$ = $\frac{1}{\cos} ^ 2 \theta$

${\cos}^{2} \theta + {\sin}^{2} \theta$$/ {\sin}^{2} \theta$ = $\frac{1}{\cos} ^ 2 \theta$

further on solving you would get both sides equal to sec^2 theta so
it is proved.