Question

In a triangle ABC, sin² A + sin² B + sin² C = 2, then the triangle is ……. 

(a) equilateral triangle 

(b) isosceles triangle 

(c) right triangle 

(d) scalene triangle

Answer 1

(c) right triangle

On simplifying we get 

sin² A + sin² B + sin² C = 2 + 2 cos A cos B cos C = 2 (given) 

⇒ cos A cos B cos C = 0 

cos A (or) cos B (or) cos C = 0 

⇒ A (or) B (or) C = π/2 

⇒ ABC (is a right angled triangle).