Question

Question #c28de

Answer 1

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.