How do you prove the identity? tan θ(tan θ+cot θ)=sec^2 θ

tan θ(tan θ+cot θ)=sec^2θ

1 Answer
May 8, 2018

We have:

#sintheta/costheta(sintheta/costheta + costheta/sintheta) = 1/cos^2theta#

#sintheta/costheta((sin^2theta+ cos^2theta)/(costhetasintheta))= 1/cos^2theta#

#sintheta(1/(cos^2thetasintheta)) = 1/cos^2theta#

#1/cos^2theta = 1/cos^2theta#

As required.

Hopefully this helps!