If the angles A , B and C of a triangle are in an arithmetic progression and if a , b and c denote the lengths of the sides opposite to A , B and C respectively, then the value of the expression c a

Question

If the angles A , B and C of a triangle are in an arithmetic progression and if a , b and c denote the lengths of the sides opposite to A , B and C respectively, then the value of the expression c a ​ sin 2 C + a c ​ sin 2 A is

TestHub · Accepted Answer

Since, A , B , C are in AP ​ ⇒ 2 B = A + C ie, ∠ B = 6 0 ∘ ∴ c a ​ ( 2 sin C cos C ) + a c ​ ( 2 sin A cos A ) = 2 k ( a cos C + c cos A ) [ using, s i n A a ​ = s i n B b ​ = s i n C c ​ = k 1 ​ ​ ] = 2 k ( b ) = 2 sin B ​ = 3 ​ [using, b = a cos C + c cos A ]

Mathematics - Properties of Triangles Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Advanced (2028)