Proving a a trigonometric identity

Question

tanx+sinx=(1+cosx)/cotx

How can I prove that the left side is equivalent to the right side using trig identities?

Answer 1

tanx + sinx = sinx/cosx + sinx = sinx/cosx + sinxcosx/cosx = (sinx + sinxcosx)/cosx = sinx(1+cosx)/cosx =

(1+cosx)/(cosx/sinx) = (1+cosx)/cotx