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sqrt((1+sin x)/(1-sin x))= tan(pi/4+x/2)...

`sqrt((1+sin x)/(1-sin x))= tan(pi/4+x/2)`

Text Solution

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`LHS = (sqrt(1+sin x))/(sqrt(1-sin x)) xx (sqrt(1+sin x))/(sqrt(1+sin x)) =((1+sin x))/(cos x) =(1- cos ((pi)/(2) +x))/(sin.((pi)/(2)+x))`
`=(2 sin^(2).((pi)/(4)+(x)/(2)))/(2 sin .((pi)/(4)+(x)/(2)) cos ((pi)/(4)+(x)/(2))) = tan ((pi)/(4) +(x)/(2)) = RHS`
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