How do you verify the identity #(2tanx)/(1+tan^2x) =sin2x#?

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Apr 30, 2015

Use the fact that:
#tanx=sinx/cosx#
and
#sin2x=2sinxcosx#
So:
#2sinx/cosx*1/(1+sin^x/cos^2x)=2sinxcosx#
#2sinx/cosx*cos^2x/(cos^2x+sin^2x)=2sinxcosx#
#2sinx/cancel(cosx)*cos^cancel(2)x/(cos^2x+sin^2x)=2sinxcosx#

But #sin^2x+cos^2x=1#
So:
#2sinxcosx=2sinxcosx#

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