Question

Verify the identity:

cos x -cox x/1-tan x = sin x cos x/sin x -cos x

Answer 1

LS = cosx = cosx/(1 - sinx/cosx))

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