How do i verify the following trig identity? (tan^2x + 1)(cos^2x - 1) = -tan^2x

1 Answer
May 25, 2018

See below.

Explanation:

tan^2x + 1 = sec^2x

sec^2x = 1/cos^2x

1/cos^2x * cos^2x - 1 = (cos^2x -1)/cos^2x

To find cos^2x -1, we can use the identity sin^2x + cos^2x = 1.

sin^2x + cos^2x = 1

cos^2x = 1 - sin^2x

cos^2x - 1 = -sin^2x

-sin^2x/cos^2x = -tan^2x