Question

1 + tan² theta is equal to?​

Answer 1

Answer:

1 + tan² theta= sec² theta

Step-by-step explanation:

we know that the Identity is

sec² theta - tan² theta=1

Answer 2

Given:

$1 + {tan}^{2} \: theta$

To Find:

$The \: value \: of \: (1 + {tan}^{2} \: theta)$

Solution:

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

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

Since, sin^2 theta + cos^2 theta = 1

$= \frac{1}{ {cos}^{2} \: theta }$

Since, 1/cos theta = sec theta

$\frac{1}{ {cos}^{2} \: theta } = {sec}^{2} \: theta$

The value of 1 + tan² theta is equal to sec^2 theta.