Question

How do you prove the identity `cos^2theta(1 + tan^2theta) = 1`?

Answer 1

Prove `cos^2 x(1 + tan^2 x) = 1`

Explanation:

#cos^2 x(1 + sin^2 x/cos^2 x) = [cos^2 x (cos^2 x + sin^2 x)]cos^2 x = cos^2 x/cos^2 x = 1#
Reminder: `sin^2 x + cos^2 x = 1`