Buktikan identitas trigonometri di bawah ini! (1 + sin x - cos x) / (1 + sin x + cos x) + (1 + sin x + cos x) / (1 + sin x - cos x) = 2 csc x

misal
a = sin x - cos x --> a² = 1- 2 sin x cos x
b = sin x + cos x --> b² = 1 + 2 sin x cos x
.
a² +b² = 2
a+ b =  2 sin x
a.b = sin² x - cos² x= sin² x - (1 - sin² x) = 2 sin² x - 1
.
(1 + a)/(1 +b) + (1+b)/(1+ a) =
= [(1+a)²+ (1+b)²] / (1+a)(1+b)
= [1 + 2a + a² + 1 + 2b + b²] /(1 + a + b + ab)
= [2 + 2(a+b) + (a²+b²)} /(1 + (a + b) + ab)
= [2 + 2(2 sin x)+ 2] / (1 + 2 sin x + 2 sin² x -1)
= (4 + 4 sin x) / (2sin x + 2sin² x)
= 2(2 + 2 sin x) / 2 ( sin² x + sin x)
= 2 + 2 sin x / sin x (1+ sin x)
= 2(1 + sin x)/ sin x (1+sin x)
= 2/sin x = 2 (1/sin x)
= 2 csc x