Let tanα,tanβ,tanγ;α,β,γ≠(2n−1)π2,n∈N be the slopes of three line segment OA, OB and OC, respectively, where O is origin. If the circumcentre of △ABC coincides with origin and its orthocentre lies on y− axis, then the value of (cos3α+cos3β+cos3γcosαcosβcosγ)2 is equal to

Let tanα,tanβ,tanγ;α,β,γ≠(2n−1)π2,n∈N be the slopes of th

1.	Let tanα,tanβ,tanγ;α,β,γ≠(2n−1)π2,n∈N be the slopes of three line segment OA, OB and OC, respectively, where O is origin. If the circumcentre of △ABC coincides with origin and its orthocentre lies on y− axis, then the value of (cos3α+cos3β+cos3γcosαcosβcosγ)2 is equal to
Answer» Let $tan α, tan β, tan γ; α, β, γ \neq \frac{(2 n - 1) π}{2}$ , $n \in N$ be the slopes of three line segment $O A,$ $O B$ and $O C,$ respectively, where $O$ is origin. If the circumcentre of $△ A B C$ coincides with origin and its orthocentre lies on $y -$ axis, then the value of ${(\frac{cos 3 α + cos 3 β + cos 3 γ}{cos α cos β cos γ})}^{2}$ is equal to