Question

(sinx-2+(1/sinx))/(sinx-(1/sinx))=(sinx-1)/(sinx+1)

Answer 1

Develop the left side:
Numerator: (sin x - 2 + 1/sin x) = (sin^2x - 2sin x + 1)/sin x
Denominator: (sin x - 1/sin x) = (sin^2 x - 1)/sin x
Left side: (sin x - 1)^2/(sin^2 x) - 1 = (sin x -1)/(sin x + )

Answer 2

Left side: [(sin x - 1)(sin x - 1)]/(sin x - 1)(sin x + 1) = (sin x -1)/(sin x + 1)