How do you verify the identity $(sintheta+costheta)^2-1=sin2theta$ ?

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Answer 1 · 2016-12-31T09:35:22

See proof below

We need

$sin^2theta+cos^2theta=1$

$(a+b)^2=a^2+2ab+b^2$

$2sinthetacostheta=sin2theta$

LHS is

$(sintheta+costheta)^2-1$

$=sin^2theta+2sinthetacostheta+sin^2theta-1$

$=1+2sinthetacostheta-1$

$=2sinthetacostheta$

$=sin2theta$

$=RHS$

$QED$

How do you verify the identity (sintheta+costheta)^2-1=sin2theta(sintheta+costheta)^2-1=sin2theta?