Question

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

Answer 1

Here is the answer:-

Explanation:

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

`1+sin^2theta/cos^2theta` = `1/cos^2theta`

`cos^2theta+sin^2theta` `/sin^2theta` = `1/cos^2theta`

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