Find the value of $$\operatorname{cosec}(60^{\circ}+A)-\sec(30^{\circ}-A)+\frac{\operatorname{cosec}49^{\circ}}{\sec41^{\circ}}$$.

$$\operatorname{cosec}(60^{\circ}+A)-\sec(30^{\circ}-A)+\frac{\operatorname{cosec}49^{\circ}}{\sec41^{\circ}}$$

= $$\operatorname{cosec}(60^{\circ}+A)-\sec(90^{\circ}-60^{\circ}-A)+\frac{\operatorname{cosec}49^{\circ}}{\sec\left(90-49\right)^{\circ}}$$

$$\left[\sec\left(90\ -\theta\right)=\operatorname{cosec}\theta\right]$$

= $$\operatorname{cosec}\left(60^{\circ}+A\right)-\sec\left(90^{\circ}-\left(60^{\circ}+A\right)\right)+\frac{\operatorname{cosec}49^{\circ}}{\operatorname{cosec}49^{\circ}}$$

= $$\operatorname{cosec}\left(60^{\circ}+A\right)-\operatorname{cosec}\left(60^{\circ}+A\right)+1$$

= 1

Hence, the correct answer is Option A