Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let 
, where A,B,C are angles of a triangle ABC. If the lengths of the sides opposite these angles are a,b,c respectively, then :
A
B
are in A.P.
C
are in A.P.
D
are in A.P.
Text Solution
Verified by ExpertsThe correct answer is:
B
As A,B,C are angles of triangle
A + B + C = π
A = π − (B + C)
So,sinA = sin(B + C)…(1)
Similarly sinB = sin(A + C)…(2)
From (1) and (2)
sin(C + B) ⋅ sin(C − B) = sin(A − C) sin(A + C) sin 2 C − sin 2 B = sin 2 A − sin 2 C
{ ∵ sin(x + y) sin(x − y) = sin 2 x − sin 2 y} 2 sin 2 C = sin 2 A + sin 2 B
By sine rule 2c 2 = a 2 + b 2
⇒ b 2 , c 2 and a 2 are in A.P.
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