Let tan α , tan β and tan γ ; α , β , γ ≠ ( 2 n - 1 ) π 2 , n ∈ N be the slopes of the three line segments O A , O B and O C , respectively, where O is origin. If circumcentre of Δ A B C coincides with origin and its orthocentre lies on y -axis, then the value of cos 3 α + cos 3 β + cos 3 γ cos α · cos β · cos γ 2 is equal to

Step-by-step solution

Given, the slopes of the line segments O A ,   O B and O C are respectively, tan α ,   tan β   &   tan γ , then by parametric form the coordinates of the points A ,   B   &   C can be taken respectively as O A cos α ,   O A sin α ,   O B cos β ,   O B sin β   &   O C cos γ ,   O C sin γ . Given, the circumcentre of the ∆ A B C is at origin and we know that the circumcentre is equidistant f