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