How do you use the double angle formula to verify #tan^2x=(1-cos2x)/(1+cos2x)#?

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Answer 1 · 2017-01-12T13:51:19

See proof below

#tanx=sinx/cosx#

#cos2x=1-2sin^2x#

#cos2x=2cos^2x-1#

#RHS=(1-cos2x)/(1+cos2x)#

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

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

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

#=tan^2x#

#=LHS#

#QED#