What is 1 + tan^2x equal to?

Answer 1

sec^2(theta)

= 1 + tan^2(theta)

1/cos^2(theta) = 1 + sin^2(theta)/cos^2(theta)

multiply both sides by cos^2(theta)

1 = cos^2(theta) + sin^2(theta) which is a version of the Pythagorean Theorem on a unit circle