How do you verify the identity: $(sinx+cosx)^2=1+sin2x$ ?

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Answer 1 · 2015-07-04T05:32:46

By expanding LHS term and applying Pythagoras identity .

LHS= $(sinx+cosx)^2$

$LHS=sin^2x+cos^2x+2sinxcosx$

$LHS=1+sin2x$ since $sin^2x+cos^2x=1 & sin2x=2sinxcosx$

$LHS=RHS$

hence proved

How do you verify the identity: (sinx+cosx)^2=1+sin2x(sinx+cosx)^2=1+sin2x?