\(\sqrt{\frac{1-cosθ}{1+cosθ}}\) = \(\sqrt{\frac{1-cosθ}{1+cosθ}\times\frac{1-cosθ}{1-cosθ}}\)
= \(\sqrt{\frac{(1-cosθ)^2}{1-cos^2θ}}\)
= \(\sqrt{\frac{(1-cosθ)^2}{sin^2θ}}\)
= \(\frac{1-cosθ}{sinθ}\)
= \(\frac{1}{sinθ}-\frac{cosθ}{sinθ}\)
= cosecθ-cotθ
Hence Proved.