sorry the first one I put in had a typo

Question

cosx/1-tanx + sinx/1-cotx = sinx +cosx

Answer 1

prove that it is an identity I assume ??

General rule to start:
1. begin with the complicated side and simplify it
2. change all trig ratios to sines and cosines if possible, unless an obvious relation can be seen

LS
= cosx/(1-sinx/cosx) + sinx/(1 - cosx/sinx)
= cosx/[(cosx - sinx)/cosx] + sinx/[(sinx-cosx)/sinx]
= cosx (cosx)/(cosx - sinx) - sinx (cosx - sinx)
= (cos^2 x - sin^2 x)/(cosx - sinx)
= (cosx - sinx)(cosx+ sinx)/(cosx - sinx)
= cosx + sinx
= RS

Answer 2

5th last line should say

= cosx (cosx)/(cosx - sinx) - sinx (sinx)(cosx - sinx)

Answer 3

Thanks!