In Δ ABC having vertices A(a cosθ1,a sinθ1),B(a cosθ2,a sinθ2) and C(a cosθ3,a sinθ3) is equilateral, then which of the followings is/are true?
In equilateral triangle; AB = BC = AC
AB=√(a cosθ2−a cos θ1)2+(a sinθ2−a sinθ1)2
=√a2{1+1−2(sinθ1sinθ2+cosθ1cosθ2)}
=a√2−2cos(θ1−θ2)
=2a∣∣sin(θ1−θ22)∣∣
Similarly: BC=2a∣∣sin(θ3−θ12)∣∣
∴∣∣sin(θ1−θ22)∣∣=sin∣∣(θ2−θ32)∣∣=∣∣sin(θ3−θ12)∣∣ ....option (d)