# How do you prove 1+tan^2 (x) = sec^2 (x)?

Oct 1, 2016

See explanation...

#### Explanation:

Starting from:

${\cos}^{2} \left(x\right) + {\sin}^{2} \left(x\right) = 1$

Divide both sides by ${\cos}^{2} \left(x\right)$ to get:

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

which simplifies to:

$1 + {\tan}^{2} \left(x\right) = {\sec}^{2} \left(x\right)$