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Find the maximum vertical distance betwe...

Find the maximum vertical distance between the graphs `y=2+3sinx` and `y=4cos x-3`.

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We have `y_(1)=2+3sin x` and `y_(2)=4 cos x -3`
`therefore y_(1)-y_(2)=3sin x-4cos x+5`
`therefore (y_(1)-y_(2))_("max")=sqrt(3^(2)+(-4)^(2))+5=10`
So , maximum vertical distance between the graphs is 10.
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