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minimum-value-of-f-x-256-sin-2-x-324-cosec-2-x-x-R-

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Question Number 159641 by tounghoungko last updated on 19/Nov/21
minimum value of f(x)=256 sin^2 (x)+324 cosec^2 (x) ∀x∈ R
minimumvalueoff(x)=256sin2(x)+324cosec2(x)∀x∈R
Commented by gsk2684 last updated on 19/Nov/21
minimum value of f(x)=256 sin^2 (x)+324 cosec^2 (x) ∀x∈ R f(x)=256 sin^2 (x)+324 cosec^2 (x) f(x)=(16 sin x)^2 +(18 cosec x)^2 f(x)=(16 sin x−18 cosec x)^2 +2(16 sin x)(18cosec x) f(x)=(16 sin x−18 cosec x)^2 +576 min f(x) is 576 or f(x)=256 sin^2 (x)+324 cosec^2 (x) ≥2(√(256sin^2 x . 324cosec^2 x)) =2(16)(18) =576 min f(x) is 576
minimumvalueoff(x)=256sin2(x)+324cosec2(x)∀x∈Rf(x)=256sin2(x)+324cosec2(x)f(x)=(16sinx)2+(18cosecx)2f(x)=(16sinx−18cosecx)2+2(16sinx)(18cosecx)f(x)=(16sinx−18cosecx)2+576minf(x)is576orf(x)=256sin2(x)+324cosec2(x)⩾2256sin2x.324cosec2x=2(16)(18)=576minf(x)is576

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