Basic Identities question. PRECALC

(1 - cos) / sin = sin / ( 1 + cos) 

Cross Multiply: 

(1 - cos)(1 + cos) = sin^2 

1 - cos^2 = sin^2 

1 = cos^2 + sin^2 

1 = 1

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

[ (1/cos - tan) * (tan)] * [cos]  =

[sin / cos^2 - sin^2/cos^2 ] * [cos]  =

(sin/cos  - sin^2/cos]  =

tan - tan*sin =

tan (1 - sin)