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

Solution (By Examveda Team)

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