How do you use the double angle or half angle formulas to simplify (sinx-cosx)^2?

1 Answer
Oct 26, 2015

1-sin(2x)

Explanation:

Expand.

[1]" "(sinx-cosx)^2

[2]" "=sin^2x-2sinxcosx+cos^2x

Pythagorean Identity: sin^2alpha+cos^2alpha=1

[3]" "=(sin^2x+cos^2x)-2sinxcosx

[4]" "=1-2sinxcosx

Double Angle Identity: 2sinalphacosalpha=sin(2alpha)

[5]" "=color(blue)(1-sin(2x))