How do you verify the identity? of 1- tan^2x = 2 -sec^2x

1 Answer
Apr 12, 2018

I personally find it always helpful to convert to sine and cosine.

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

#(cos^2x- sin^2x)/cos^2x = (2cos^2x- 1)/cos^2x#

Recall that #sin^2x= 1 - cos^2x#.

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

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

#LHS = RHS#

As required.

Hopefully this helps!