Question

Prove the following identity tan x cos x/sin x=1/sin x cos x

Answer 1

tan x cos x/sin x=1/sin x cos x
or
tan x cos x/sin x=1/(sin x cos x) ?

For either case,
LS = tanx(cosx/sinx)
= tanx cotx
= 1

For any given x, RS ≠ 1

Your equation is NOT an identity, so it cannot be proven to be true.

Answer 2

Its tan x cos x/sin x=1/sin x cos x

Answer 3

yup, that's what you typed the first time.
And I pointed out to you that that is not an identity.