If the range of f(θ)=(sin^4 θ+3 cos^2 θ)/(sin^4 θ+cos^2 θ), θ ∈ R is [α, β] , then the sum of the infinite G.P., whose first term is 64 and the common…

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If the range of f(θ)=(sin^4 θ+3 cos^2 θ)/(sin^4 θ+cos^2 θ), θ ∈ R is [α, β] , then the sum of the infinite G.P., whose first term is 64 and the common ratio is (α)/(β) , is equal to________

MARKS Content Team · Accepted Answer

Correct answer: 96. f(θ)=(sin^4 θ+3 cos^2 θ)/(sin^4 θ+cos^2 θ) f(θ)=1+(2 cos^2 θ)/(sin^4 θ+cos^2 θ) f(θ)=(2 cos^2 θ)/(cos^4 θ-cos^2 θ+1)+1 f(θ)=2/(cos^2 θ+sec^2 θ-1)+1 .f(θ) |_min. =1 f(θ)_max. =3 S=64/(1-1 / 3)=96

If the range of $f(\theta)=\frac{\sin ^4 \theta+3 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta}, \theta \in \mathbb{R}$ is $[\alpha, \beta]$, then the sum of the infinite G.P., whose first term is 64 and the common ratio is $\frac{\alpha}{\beta}$, is equal to________

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