In a ∆ABC, if sin 2 A + sin 2 B = sin 2 C, show that the triangle is right angled.

Question

Philoid · Accepted Answer

Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get

So by considering the given condition, we get

sin² A + sin² B = sin² C

Substituting the values from equation (i), we get

This is Pythagoras theorem; hence the given triangle ABC is right - angles triangle

Hence proved