Prove trigo identities?

Question

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

Answer 1

LHS

= cos x / (1- sin x) - 1/cos x

= cos x (1 + sin x) / (1 - sin x)(1 + sin x) - 1/cos x

= cos x (1 + sin x) / 1 - sin² x) - 1 / cos x

= cos x (1 + sin x) / cos² x - 1 / cos x

= (1 + sin x) / cos x - 1 / cos x

= 1 / cos x + sin x / cos x - 11 / cos x

= sin x / cos x

= tan x

= RHS.

Answer 2

repost with parentheses. i do not know what the equation is, so it cannot be answered by me.

make it a good day

Answer 3

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

[cos^2 x - (1-sin x)] / (1- sin x)(cos x) = tan x

(cos^2 x - 1 + sin x) / (1- sin x)(cos x) = tan x

(cos^2 x - (cos^2 x + sin^2x) + sin x) / (1- sin x)(cos x) = tan x

(cos^2 x - cos^2 x - sin^2x + sin x) / (1- sin x)(cos x) = tan x

(- sin^2x + sin x) / (1- sin x)(cos x) = tan x

[sin x( -sin x +1)] / (1 -sin x)(cos x) = tan x

[sin x( 1-sin x )] / (1 -sin x)(cos x) = tan x

sin x / cos x = tan x

tan x = tan x