Explanation:

Sin² A + sin² B + sin² C = 2 (cos² A + cos² B + cos² C)

3 – (cos² A + cos² B + cos² C) = 2 (cos² A + cos² B + cos² C)

Or (cos² A + cos² B + cos² C) = 1

Or 1+cos2A / 2  + 1+cos2B / 2 + 1+ cos2C / 2 = 1

Or 3 + (cos2A + cos2B + cos2C) = 2

Or 2 cos (A + B) cos (A–B) +cos 2C = -1

A + B + C = π

Or A + B = π – C → (1)

∴ 2 cos (π – C) cos (A – B) + cos 2C = -1

– 2 cos C cos (A – B) = - (1 + cos 2C)

Or 2 cos C cos (A – B) = 2 cos² C

Or cos (A – B) = cos C

⇒ A – B = C

Putting in (1):

A = π/2