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

Explanation

`f(x)=(3sinx-4cosx-10)(3sinx+4cosx-10)`

`f(x)=[(3sinx-10)-4cosx][(3sinx-10)+4cosx]`

`f(x)=(3sinx-10)^2-16cos^2x`

`f(x)=9sin^2x+100-60sinx-16(1-sin^2x)`

`f(x)=25sin^2x+84-60sinx`

`f(x)=(5sinx-6)^2+48`

at sinx=1

`f(x)=(5-6)^2+48=49`

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