If A is an acute angle and cotA + cosecA = 3, then the value of sinA is?

Answer: Option C

$$\begin{array}{rl}& \text{According to the question,}\\ & \text{cosec A}+\text{cot A}=3\\ & \text{cosec A}-\text{cot A}=\frac{1}{3}\\ & \overline{2\text{cosec A}=\frac{10}{3}}\\ & \text{cosec A}=\frac{10}{6}\\ & \text{sin A}=\frac{6}{10}\\ & \text{sin A}=\frac{3}{5}\end{array}$$