# Question c28de

Jul 3, 2016

see explanation

#### Explanation:

If we can show that the left side can be expressed in the form of the right side then it is verified.

left side $= {\left(\sin x - \cos x\right)}^{2} = \left(\sin x - \cos x\right) \left(\sin x - \cos x\right)$

Expand using FOIL

$= {\sin}^{2} x - \sin x \cos x - \sin x \cos x + {\cos}^{2} x$

$= {\sin}^{2} x + {\cos}^{2} x - 2 \sin x \cos x$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminders}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\sin}^{2} x + {\cos}^{2} x = 1} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

color(red)(|bar(ul(color(white)(a/a)color(black) (sin2x=2sinxcosx)color(white)(a/a)|)))#

$\Rightarrow {\sin}^{2} x + {\cos}^{2} x - 2 \sin x \cos x = 1 - \sin 2 x$

now 1 - sin2x is what is on the right side , hence verified.