Question

proving identities:
(tan/sec) - (cot/csc) = sin - cos

Answer 1

(tan x /sec x) - (cot x /csc x) = sin x - cos x

( [sinx/cosx] / [1 / cos x] ) - ( [cos x/ sin x ] / [ 1 / sin x] ) = sin x - cos x

( [sinx/cosx] * [cos x / 1] ) - ( [cos x/ sin x ] * [ sin x /1] ) = sin x - cos x

( sin x ) - ( cos x ) = sin x - cos x

Answer 2

I put everything in terms of sines and cosines on the left side, canceled things out...

see what I am doing?

Answer 3

got it. thanks @SolomonZelman