How do you simplify $(sinx-cosx)^2+sin2x$ ?

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Answer 1 · 2018-04-15T21:02:22

$1$

Expand $(sinx-cosx)^2$ using the FOIL method:

$(sinx-cosx)^2=(sinx-cosx)(sinx-cosx)$

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

Thus, we're left with

$sin^2x-2sinxcosx+cos^2x+sin2x$

Recall the identity $sin2x=2sinxcosx.$ Then, we have

$sin^2x-cancel(sin2x)+cos^2x+cancel(sin2x)$

$sin^2x+cos^2x$

And, recalling that $sin^2x+cos^2x=1,$ the simplified form is

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How do you simplify (sinx-cosx)^2+sin2x(sinx-cosx)^2+sin2x?