Let \tan \alpha, \tan \beta and \tan \gamma, \alpha, \beta, \gamma \neq \frac{(2 n-1) \pi}{2}, n \in N be the slopes of three line segments O A, O B and O C, respectively, where O is origin. If circumcentre of \triangle A B C coincides with origin and its orthocentre lies on y-axis, then the value of (\frac{\cos 3 \alpha+\cos 3 \beta+\cos 3 \gamma}{\cos \alpha \cos \beta \cos \gamma})^{2} is equal to ......... [17 Mar 2021 Shift 2]

Straight Lines and Pair of Straight Lines Part 1

Section: Mathematics

Question : 21 of 100

Marks: +1, -0

Let tan‌α,tan‌β and tan‌γ,α,β,γ≠‌

(2n−1)π

, n∈N be the slopes of three line segments OA,OB and OC, respectively, where O is origin. If circumcentre of △ABC coincides with origin and its orthocentre lies on y-axis, then the value of (‌

cos‌3‌α+cos‌3‌β+cos‌3‌γ

cos‌α‌cos‌β‌cos‌γ

)2 is equal to .........

[17 Mar 2021 Shift 2]

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