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

1.	Prove the following trigonometric identities:\(\sqrt{\frac{1+sinA}{1-sinA}}\) = secA + tanA
Answer» \(\sqrt{\frac{1+sinA}{1-sinA}}\) = \(\sqrt{\frac{1+sinA}{1-sinA}}\times \sqrt{\frac{1+sinA}{1+sinA}}\) = \(\sqrt{\frac{(1+sinA)^2}{1-sin^2A}}\) = \(\sqrt{\frac{(1+sinA)^2}{cos^2A}}\) = \(\frac{1+sinA}{cosA}\) = \(\frac{1}{cosA}+\frac{sinA}{cosA}\) = secA + tanA Hence Proved.

Prove the following trigonometric identities:\(\sqrt{\frac{1+sinA}{1-sinA}}\) = secA + tanA

Answer»

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

= \(\sqrt{\frac{(1+sinA)^2}{1-sin^2A}}\)

= \(\sqrt{\frac{(1+sinA)^2}{cos^2A}}\)

= \(\frac{1+sinA}{cosA}\)

= \(\frac{1}{cosA}+\frac{sinA}{cosA}\)

= secA + tanA

Hence Proved.