(sinx-cosx)²=1-2 sinx cosx prove?

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Answer 1 · 2018-03-22T09:07:40

Don't forget the middle term and the trig equations.

#Sin^2(x)+Cos^2(x)=1#
#Sin(2x)=2Sin(x)Cos(x)#- If you wanted further simplificaton

#(Sin(x)-Cos(x))^2=Sin^2(x)-2Sin(x)Cos(x)+Cos^2(x)#

Hence:
#Sin^2(x)+Cos^2(x)=1#

#1-2Sin(x)Cos(x)#, which is your desired answer, but it could be further simplified to:

#1-Sin(2x)#

Answer 2 · 2018-03-22T09:08:11

See the explanation

#(sinx-cosx)^2#

#=> (sinx)^2+(cosx)^2-2xxsinx xxcosx#

#=> sin^2x+cos^2x-2sinxcosx#

We know , #sin^2x+cos^2x=1#

Substitute #1# for #sin^2x+cos^2x#

#=> 1-2sinxcosx#

Hence proved