Verify the trigonometric identity 1 sin x 1 sin x sec x

Verify the trigonometric identity:

1 + sin x /1 - sin x = (sec x + tan x)

Solution

(1+sin x)/(1-sin x)= (sec x + tan x)

Starting with the left side

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

Multiplying both top and bottom by 1+sinx

(1+ sin x)(1+sin x)/(1-sin²x)

(1+ sinx)²/cos²x

((1+ sinx)/ cos x)²= (1/cosx + sin x/ cos x)²= (sec x + tan x)² that is equal to right side