How do you perform multiplication and use the fundamental identities to simplify $(sinx+cosx)^2$ ?

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Answer 1 · 2017-01-13T02:02:07

$(sinx+cosx)^2 = 1+sin2x$

$(sinx+cosx)^2 = (sinx+cosx)(sinx+cosx)$
$" "= sin^2x + 2sinxcosx+cos^2x$
$" "= (sin^2x +cos^2x) + 2sinxcosx$
$" "= 1+sin2x$

How do you perform multiplication and use the fundamental identities to simplify (sinx+cosx)^2(sinx+cosx)^2?