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