What is the  value of $\sqrt{\frac{cosec A+1}{cosecA-1}}+\sqrt{\frac{cosecA-1}{cosecA +1}}$

2 sec A 

$\sqrt{\frac{cosec A+1}{cosecA-1}}+\sqrt{\frac{cosecA-1}{cosecA +1}}$

= \(\frac{√(cosecA + 1 )² + √(cosecA - 1 )² }{ √( cosecA - 1 ) . √( cosecA + 1 ) }\)

= \(\frac{(cosecA + 1 ) + (cosecA - 1 ) }{  √(cosec²A - 1) }\)

{ using, cosec²A - cot²A = 1 }

= \(\frac{2cosecA  ) }{  √cot²A }\)

= \(\frac{2cosecA  ) }{  cotA }\)

= 2 secA