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Show that 5x le 8 sin x-sin 2x le 6x for x le x le (pi)/(3) |
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Answer» Solution :Let f(x) =8 sinx - sin 2x f(x)=8 cos x -2 cos 2x f(x) =-8sin x +4 sin 2x =-8 sinx (1-cosx) `therefore f(x)lt0in [(0,(pi)/(3))]` f(x) is decreasing function in `[(0,(pi)/(3))]` `f(pi)/(3)lef(x)lef(0)` `5lef(x)LE6 in [(0,(ppi)/(3))]` `5xlef(x)le6x in [(0,(pi)/(3))` |
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