How do you prove #tan(2x) = (2tan(x))/(1-tan^2 x)#?

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Apr 14, 2016

Answer:

Use
#tan x=sinx/cos x, sin 2x = 2 sin x cos x and cos 2x = cos^2x-sin^2x#, for the right hand side expression

Explanation:

#2 tan x/(1-tan^2x)=(2sin x/cos x)/(1-(sin^2x/cos^2x)#

#=2 sin x cos x/(cos^2x-sin^2x)#
#=(sin 2x)/(cos 2x)=tan 2x#

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