Functional Trigonometry

Geometry Level 3

f(θ)=(cot2θ+5)(cot2θ+10)cot2θ+1\large f(\theta)=\dfrac{(\cot^2\theta+5)(\cot^2\theta+10)}{\cot^2\theta+1}

Find the range of f(θ)f(\theta) for all real values of θ\theta.


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