Q2 Q2 If (a cos θ1, a sin θ2), (a cos θ2, a sin θ2) and (a cos - Maths - Straight Lines

Question

Q2

Q2 If (a cos θ 1 ,   a   sin   θ 2 ), (a
cos θ 2, a sin θ 2) and (a cos
θ 3, a sin θ 3) represents the
vertices of an equilateral triangle inscribed inscribed in a
circle, then

(A) cos θ 1 + cos θ 2 + cos
θ 3 = 0 (B) sin θ 1 + sin θ
2 + sin θ 3 = 0

(C) tan θ 1 + tan θ 2 + tan
θ 3 = 0 (D) cot θ 1 + cot θ
2 + cot θ 3 = 0

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

acosθ1,asinθ1,acosθ2,asinθ2,acosθ3,asinθ3 are vertices of triangle
Note that acosθ1,asinθ1,acosθ2,asinθ2,acosθ3,asinθ3 are alsoparametric coordinates of circle x2+y2=a2Hence circumcentre of triangle is 0,0As triangle is equilateral, hence circumcentre will be same as centroid
⇒Centroid=0,0⇒acosθ1+acosθ2+acosθ33,asinθ1+asinθ2+asinθ33=0,0⇒acosθ1+acosθ2+acosθ3=0 and asinθ1+asinθ2+asinθ=0

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