If $\frac{cosA}{cosecA+1}+\frac{cosA}{cosecA-1}= 2, 0° ≤ A ≤ 90°$, then A is equal to :

45°

Given :-

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

\(\frac{cosA ( cosecA-1) + cosA(cosecA +1 ) }{cosec²A - 1 }\)= 2

We know , { cosec²A - 1 = cot²A  }

\(\frac{2cosA.cosecA }{cot²A  }\)= 2

\(\frac{cosA.cosecA }{cos²A / sin²A }\) = 1

\(\frac{cosecA }{cosA / sin²A }\) = 1

tanA = 1       

Ans we know that , tan45º = 1

So, A =  45º