cosxsinxcotx+sinxsin(-x)

Answer 1

using 3 identies

1. cotx = cosx/sinx
2. sin(-x) = -sinx
3. cos^2 x - sin^2 x = cos 2x
we get
cosxsinxcotx+sinxsin(-x)
= cosxsinxcosx/sinx - sinxsinx
= cos^2 x - sin^2 x
= cos 2x