To Prove: \(\sqrt{\frac{1+sinx}{1-sinx}}=tan(\frac{\pi}{4}+\frac{x}{2})\)
Proof: Consider, L.H.S = \(\sqrt{\frac{1+sinx}{1-sinx}}\)
Multiply and divide L.H.S = \(\sqrt{1+sinx}\)
Multiply and divide the above with cos\(\frac{x}{2}\)
Here, since tan\(\frac{\pi}{4}\) = 1
Here, since tan\(\frac{\pi}{4}\) = 1
Since, L.H.S = R.H.S, Hence proved.