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

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

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

Answer»

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

= \(\frac{cosθ(1-sinθ)}{1-sin^2θ}\)

= \(\frac{cosθ(1-sinθ)}{cos^2θ}\)

= \(\frac{1-sinθ}{cosθ}\)

Hence Proved.