How do you prove tan(2theta)=2/(cottheta-tantheta)?

1 Answer
Oct 7, 2016

see below

Explanation:

tan 2 theta = 2/(cot theta-tan theta)

Right Side :=2/(cot theta-tan theta)

=2/(costheta/sin theta - sin theta/cos theta)

=2/((cos^2theta-sin^2theta)/(sin theta cos theta)

=2 * (sin theta cos theta)/(cos^2theta-sin^2theta)

=(2 sin theta cos theta)/(cos^2theta-sin^2theta)

=sin(2theta)/cos(2theta)

=tan ( 2 theta)

:. = Left Side