If circumcentre of an equilateral triangle inscribed in + = 1, with vertices having eccentric ang…

Question

If circumcentre of an equilateral triangle inscribed in  +  = 1, with vertices having eccentric angles α , β , γ respectively is (x 1 , y 1 ), then find Σ cos α cos β + Σ sin α sin β .

CGP EDU Academic Team · Accepted Answer

The correct answer is CHECK THE SOLUTION..  +  – 
Sol. Now x 1 =  (cos α + cos β + cos γ )
y 1 =  [sin α + sin β + sin γ ]
⇒  +  =  + 
⇒  +  = 1 + 1 + 1 + 2 [cos α cos β + cos β cos γ + cos γ cos α
+ sin α sin β + sin β sin γ + sin γ sin α ]
⇒ ∑ cos α cos β + ∑ sin α sin β =  +  –

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