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Prove that

\(\sqrt{\frac{1+sinx}{1-sinx}}=tan(\frac{\pi}{4}+\frac{x}{2})\)

√1 + sinx/1 - sinx = tan(π/4 + x/2)

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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.

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