The base of a triangle is divided into three equal parts

MATHEMATICS · Subjective · ISC · Mathematics · Sets and Functions · Sets and Functions

Problem

The base of a triangle is divided into three equal parts. If θ1\theta_1, θ2\theta_2, and θ3\theta_3 are the angles subtended by these parts at the vertex, prove that (cot⁡θ1+cot⁡θ2)(cot⁡θ2+cot⁡θ3)=4csc⁡2θ2(\cot\theta_1+\cot\theta_2)(\cot\theta_2+\cot\theta_3)=4\csc^2\theta_2.

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