# How do you simplify (sinX-cosX)^2?

Aug 20, 2015

${\left(\sin X - \cos X\right)}^{2} = 1 - \sin 2 X$
${\sin}^{2} A + {\cos}^{2} A = 1$
$\sin 2 A = 2 \sin A \cos A$
 (sinX-cosX)^2 = sin^2 X -2sin X cos X + cos^2 X = 1-2sin XcosX = 1-sin2X