Question

How do you simplify the expression `(sin^2theta+cos^2theta)/cos^2theta`?

Answer 1

`=> (1/cos^2 theta) = sec^2theta = (1 + tan^2 theta)`

Explanation:

Kindly remember the following identities while solving this problem.

`sin^2theta + cos^2 theta = 1, 1 + tan ^2 theta = sec ^2 theta, sec theta = 1/ cos theta`

`cancel(sin^2 theta + cos^2 theta)^color(red)1 / cos^2 theta`

`=> (1/cos^2 theta) = sec^2theta = (1 + tan^2 theta)`