5sin

^{2}x+4cos^{2}x5sin^{2}x+4cos^{2}x

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5sin^{2} x+4cos^{2} x =

5sin^{2} x+ 4(1-sin^{2}x) =

sin^{2}x + 4 = The minimum value of this expression is 4 no matter the value of x. It occurs when x=0

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