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The minimum value of sqrt((3sin x-4cosx-...

The minimum value of `sqrt((3sin x-4cosx-10(3sinx+4cosx-1))` is ________

Text Solution

Verified by Experts

The correct Answer is:
7
`f(x) =9sin^2x-16cos^2x-10(3sinx-4cosx)-10(3sinx+4cosx)+100`
`25 sin^2x-16cos^2x+84`
`=(5sinx-6)^2+48`
The minimum value of f(x) occurs when sin x = 1
Therefore , the minimum value of `sqrt(f(x)) is 7`.
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