Question

If in a triangle sinA : sinC = sin(A − B) : sin(B − C) then  a² :b² :c² 

(A) Are in A.P.

(B) Are in G.P.

(C) Are in H.P. 

(D) None of these

Answer 1

Correct option (A) Are in A.P

Explanation:

(sinA sin(B - C))/(sinC sin(A - B)) = 1

L.H.S = (sin(B + C)sin(B - C))/(sin(A + B)sin(A - B) 

= (cos2B - cos2C)/(cos2A - cos2B) = 1

⇒ 2sin²B = sin²A + sin²C ⇒ 2b² = a² + c²