How do you verify the identity (1+tan^2theta)/(1-tan^2theta)=1/(2cos^2theta-1)?

1 Answer
Aug 7, 2016

L.H.S=R.H.S.

Explanation:

Since sin^2 theta+cos^2 theta=1
L.H.S.=(1+tan^2 theta)/(1-tan^2 theta)
=(1+sin^2 theta/cos^2 theta)/(1-sin^2theta/cos^2 theta)
=((cos^2 theta+sin^2 theta)/(cancelcos^2 theta))/((cos^2 theta-sin^2 theta)/(cancelcos^2theta)
=(cos^2 theta+sin^2 theta)/(cos^2 theta-sin^2 theta)
=1/(cos^2 theta-sin^2 theta)
=1/(cos^2 theta-(1-cos^2 theta)
=1/(cos^2 theta+cos^2 theta-1)
=1/(2cos^2 theta-1)
Hence
L.H.S=R.H.S.