1.

Show that 5x le 8 sin x-sin 2x le 6x for x le x le (pi)/(3)

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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