What is the value of the following in terms of trigonometric ratios?

$\frac{sinA}{1+cosA}+\frac{1+cosA}{sinA}$

2 cosec A

\(\frac{ sinA}{1 + cosA}\) + \(\frac{ 1 + cosA}{sinA}\)

= \(\frac{ sin²A + ( 1 + cos A )²}{sinA(1 + cosA)}\) 

= \(\frac{ sin²A + 1 + cos² A + 2cosA}{sinA(1 + cosA)}\)

{ using , sin²A + cos²A = 1 }

= \(\frac{ 1 + 1 + 2cosA}{sinA(1 + cosA)}\)

= \(\frac{2( 1 + cosA)}{sinA(1 + cosA)}\)

= 2 cosecA