Question

Prove that √1+ sin x/1-sin x = sec x + tan x

Answer 1

Solution:-

To Prove:-

√[(1+ sin x)/(1-sin x)] = (sec x + tan x)

Proof:-

L.H.S.

√[(1+ sin x)/(1-sin x )]

On Rationalising we get,

=> √[(1+ sin x)/(1-sin x)] × √[(1+ sin x)/(1+ sin x )]

=> √( 1+ sin x)²/ √(1² - sin²x)

=> ( 1 + sin x)/ √cos² x

=> ( 1+ sin x)/ cos x

=> 1/ cos x + sin x/cos x

=> Sec x + Tan x.

Hence Proved!!