Prove this identity:?

Question

Prove the identity (sec x + tan x)^2 = (1 + sin x) / (1 - sin x)

Answer 1

LHS
(1 / cos x + sin x / cos x) ²
(1 + sin x) ² / cos ² x
(1 + sin x) ² / (1 - sin ² x)
(1 + sin x) ² / (1 - sin x)(1 + sin x)
(1 + sin x) / (1 - sin x)

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

LHS = RHS

Answer 2

(sec x + tan x)^ 2 = (1+sin x) / ( 1 -sin x)
sec ^2 x + 2 sec x tan x + tan^2 x
(1/ cos^2 x) + 2 (sin x/ cos^2 x) + (sin^2 x/cos^2 x)
(1+2sinx + sin^2x)/ (cos^2 x)
(1+ sin x)^2 / (1-sin^2 x) cancel the common 1+ sin x
(1+ sin x) / ( 1-sin x)