If A is an acute angle and cot A + cosec A = 3, then the

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cosec²A – cot² A = 1
(cosec A + cot A) (cosec A – cot A) = 1

cosec A – cot A =	1
	3

cosec A + cot A = 3 On adding,

2 cosec A =	1	+ 3 =	1 + 9	=	10
	3		3		3

⇒ cosec A =	10	=	5
	3 × 2		3

∴ sin A =	3
	5