Question

How do you simplify the expression `1+tan^2x`?

Answer 1

`1+tan^2x=sec^2x`

Explanation:

Change to sines and cosines then simplify.

`1+tan^2x=1+(sin^2x)/cos^2x`

`=(cos^2x+sin^2x)/cos^2x`

but `cos^2x+sin^2x=1`

we have`:.` `1+tan^2x=1/cos^2x=sec^2x`