Question

root 1 + tan square theta is equal to​

Answer 1

Answer:

sec square theta.......

Answer 2

$\displaystyle \sf{ \sqrt{1 + {tan}^{2} \theta} } = {sec}^{} \theta$

Given :

$\displaystyle \sf{ \sqrt{1 + {tan}^{2} \theta} }$

To find :

Simplify the given expression

Formula :

$\displaystyle \sf{ 1 + {tan}^{2} \theta} = {sec}^{2} \theta$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \sqrt{1 + {tan}^{2} \theta} }$

Step 2 of 2 :

Simplify the given expression

We use the formula

$\displaystyle \sf{ 1 + {tan}^{2} \theta} = {sec}^{2} \theta$

The given expression

$\displaystyle \sf{ = \sqrt{1 + {tan}^{2} \theta} }$

$\displaystyle \sf{ = \sqrt{ {sec}^{2} \theta} }$

$\displaystyle \sf{ = sec \: \theta}$