The   value of $ \sqrt{\frac{1+cosA}{1-cosA}} $ is :

sec A - tan A cosec A + cot A  sec A + tan A cosec A - cot A

cosec A + cot A

$\sqrt{\frac{1+cosA}{1-cosA}}$ Multiply and divide by ( 1 + cosA ) = $\sqrt{\frac{1+cosA}{1-cosA}}$  × $\sqrt{\frac{1+cosA}{1+cosA}}$ = $\sqrt{\frac{(1+cosA)2}{sin2A}}$ =  \(\frac{( 1 + cosA ) }{sinA}\) = cosecA + cotA