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Straight Lines and Pair of Straight Lines question

2021 · 17 Mar · Shift 2 · Q36
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  5. /2021 · 17 Mar · Shift 2 · Q36

Straight Lines and Pair of Straight Lines question

2021 · 17 Mar · Shift 2 · Q36

JEE MainMathematicsStraight Lines and Pair of Straight LinesNumerical+4 / −1
Let tan α\alphaα, tan β\betaβ and tan γ\gammaγ; α\alphaα, β\betaβ, γe(2n−1)π2\gamma e{{(2n - 1)\pi } \over 2}γe2(2n−1)π​, n ∈\in∈ N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of Δ\DeltaΔ ABC coincides with origin and its orthocentre lies on y-axis, then the value of (cos⁡3α+cos⁡3β+cos⁡3γcos⁡αcos⁡βcos⁡γ)2{\left( {{{\cos 3\alpha + \cos 3\beta + \cos 3\gamma } \over {\cos \alpha \cos \beta \cos \gamma }}} \right)^2}(cosαcosβcosγcos3α+cos3β+cos3γ​)2 is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
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