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

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Answer 1 · 2016-10-07T17:50:27

see below

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

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

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