Correct Answer – A
We have , `sin x – sin 2x + sin 3x = 0`
`rArr 2 sin ((x + 3x)/(2)) cos((x-3x)/(2)) – sin 2x = 0`
`[because sin C + sin D = 2 sin((C+D)/(2)) cos ((C-D)/(2))]`
`rArr 2 sin 2x cos x – sin 2x = 0″ “[because cos (-theta) = cos theat]`
`rArr sin 2x (2cos x-1)=0`
`rArr sin 2x=0 or 2 cos x – 1 =0`
`2x = 0, pi,……or cos x =(1)/(2)`
`rArr x = 0, (pi)/(2) ….or x =(pi)/(3)`
In the interval `[0,(pi)/(2))` only tow values satisfly , namely `x = 0` and ` = (pi)/(3)`.