Prove the following trigonometric identities:\(\frac{1-cosθ}{sinθ}=\

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

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

Answer»

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

= \(\frac{1-cos^2θ}{sinθ(1+cosθ)}\)

= \(\frac{sin^2θ}{sinθ(1+cosθ)}\)

= \(\frac{sinθ}{1+cosθ}\)

Hence Proved.