Making use of the following identities
sin 2x = 2 sin x cos x
cos 2x = 2 cos^2x - 1
we can write:
\(sin\ 2x-cos\ 2x=2\ sin\ x \cos\ x-2\ cos^{2}x+1 ..............(1)\)
Equation (1) can be factorized to give, on the right hand side:
2 cos x(sin x - cos x) + 1
