How do you prove the identity (sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)?

1 Answer
Mar 9, 2018

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Explanation:

Use the Property : color(blue)(sin^2x+cos^2x=1

LHS : (sinx-cosx)/(sinx+cosx)

=(sinx-cosx)/(sinx+cosx)* (sinx+cosx)/(sinx+cosx)-> multiply by conjugate

=(sin^2x-cos^2x)/(sin^2x+2sinxcosx+cos^2x)

=(sin^2x-[1-sin^2x])/([sin^2x+cos^2x]+2sinxcosx)

=(sin^2x-1+sin^2x)/(1+2sinxcosx)

=(2sin^2x-1)/(1+2sinxcosx)

=RHS