InterviewSolution
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InterviewSolution
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If `0 le x le (pi)/(2)`, then the number of value of x for which `sin x - sin 2x + sin 3x = 0`, isA. 2B. 3C. 1D. 4 |
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Answer» 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)`. |
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