KVPY #19

Geometry Level 3

Let 0<θ<π2 0 <\theta < \dfrac \pi 2 satisfying tanθ=32 \tan \theta = \sqrt{ \dfrac 32 } . Evaluate

1+2(1cosθ)+3(1cosθ)2+. 1 + 2(1-\cos \theta) + 3(1-\cos \theta)^2 + \cdots .


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