prove identity

Question

Sin2x - sinx/cosx + cos2x= sinx/cosx + 1

Answer 1

You typed it incorrectly, you must mean:

(sin(2x) - sinx)/(cosx + cos(2x)) = sinx/(cosx + 1)

LS = (2sinxcosx - sinx)/(cosx + 2cos^2 x - 1)
= sinx(2cosx -1)/( (2cosx - 1)(cosx+1) )
= sinx/(cosx + 1)
= RS