How do you verify # (1-sinx)/(1+sinx)=sec^2x-2secxtanx+tan^2x#?

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Answer 1 · 2018-04-24T07:17:09

Please see the proof below

We need

#sin^2x+cos^2x=1#

#secx=1/cosx#

#tanx=sinx/cosx#

Therefore,

#LHS=(1-sinx)/(1+sinx)#

#=((1-sinx)(1-sinx))/((1+sinx)(1-sinx))#

#=(1-sinx)^2/(1-sin^2x)#

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

#=1/cos^2x-2sinx/cos^2x+sin^2x/cos^2x#

#=sec^2x-2secxtanx+tan^2x#

#=RHS#

#QED#