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