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

1 Answer
Phiri
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#

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