(sinx-cosx)²=1-2 sinx cosx prove?

2 Answers
Mar 22, 2018

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

Explanation:

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)

Mar 22, 2018

See the explanation

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