Prove the following trigonometric identities:\(\sqrt{\frac{1-cosθ}{1+

1.	Prove the following trigonometric identities:\(\sqrt{\frac{1-cosθ}{1+cosθ}}\) = cosecθ - cotθ
Answer» \(\sqrt{\frac{1-cosθ}{1+cosθ}}\) = \(\sqrt{\frac{1-cosθ}{1+cosθ}\times\frac{1-cosθ}{1-cosθ}}\) = \(\sqrt{\frac{(1-cosθ)^2}{1-cos^2θ}}\) = \(\sqrt{\frac{(1-cosθ)^2}{sin^2θ}}\) = \(\frac{1-cosθ}{sinθ}\) = \(\frac{1}{sinθ}-\frac{cosθ}{sinθ}\) = cosecθ-cotθ Hence Proved.

Prove the following trigonometric identities:\(\sqrt{\frac{1-cosθ}{1+cosθ}}\) = cosecθ - cotθ

Answer»

\(\sqrt{\frac{1-cosθ}{1+cosθ}}\) = \(\sqrt{\frac{1-cosθ}{1+cosθ}\times\frac{1-cosθ}{1-cosθ}}\)

= \(\sqrt{\frac{(1-cosθ)^2}{1-cos^2θ}}\)

= \(\sqrt{\frac{(1-cosθ)^2}{sin^2θ}}\)

= \(\frac{1-cosθ}{sinθ}\)

= \(\frac{1}{sinθ}-\frac{cosθ}{sinθ}\)

= cosecθ-cotθ

Hence Proved.