prove (cosx-sinx)=1-2cosxsinx

Question

How can you prove this?

Answer 1

 

Using Pythagorean theorem in trigonometric form sin²x +cos²x = 1 we can rewrite right side of the identity

in the following way:

                          1-2 cosx sinx = cos²x + sin²x - 2cosxsinx = (cosx - sinx)²

I think, this is what should be. Check your statement one more time.