Question #c28de

1 Answer
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 #=(sinx-cosx)^2=(sinx-cosx)(sinx-cosx)#

Expand using FOIL

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

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

#color(orange)"Reminders"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(sin^2x+cos^2x=1)color(white)(a/a)|)))#

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

#rArrsin^2x+cos^2x-2sinxcosx=1-sin2x#

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