If in a triangle ABC, 
= 
prove that the triangle ABC is either isosceles or
right angled.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
cos A(sin B – sin C) + (sin 2B – sin 2C) = 0
⇒ cos A.(sin B – sin C) + 2 cos(B + C) sin (B – C) = 0 B + C = π – A
⇒ cos A.(sin B – sin C) – 2 cos A.sin (B – C) = 0
⇒ cos A[(sin B – sin C) – 2(sin B cos C– cos Bsin C)] = 0
⇒ either cos A = 0 ⇒ A = 90° ⇒ right angled
or (sin B – sin C) – 2(sin B cos C – cos B sin C) = 0
⇒ (b – c) – 2 
= 0
⇒ a(b – c) – 2(b 2 – c 2 ) = 0
(b – c) [a – 2(b + c)] = 0
∴ b – c = 0 ⇒ b = c ⇒ isosceles
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