What is the value of $\sqrt{\frac{cosec A+1}{cosecA-1}}+\sqrt{\frac{cosecA-1}{cosecA +1}}$
Answer & explanation
Correct answer: option 4
$\sqrt{\frac{cosec A+1}{cosecA-1}}+\sqrt{\frac{cosecA-1}{cosecA +1}}$
= \(\frac{√(cosecA + 1 )² + √(cosecA - 1 )² }{ √( cosecA - 1 ) . √( cosecA + 1 ) }\)
= \(\frac{(cosecA + 1 ) + (cosecA - 1 ) }{ √(cosec²A - 1) }\)
{ using, cosec²A - cot²A = 1 }
= \(\frac{2cosecA ) }{ √cot²A }\)
= \(\frac{2cosecA ) }{ cotA }\)
= 2 secA