Verifying trigonometric identities

Question

Find sec x if tan^2 x = 1/2

Answer 1

If tan^2 x = 1/2, then tan^2x + 1 = 3/2

tan^2x + 1 = sec^2x

so sec^2x = 3/2 and sec x = +/- sqrt(3/2) = +/- sqrt(6)/2