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

#1#