Since, A, B and C are the angles of a triangle, we have A + B + C = π.
Now, cos
2 A + cos
2 C = sin
2 B
⇒ cos
2 A + (cos
2 C - sin
2 B) = 0
⇒ cos
2 A + cos (C + B) cos (C - B) = 0
⇒ cos
2 A + cos (π - A) cos (C - B) = 0
⇒ cos
2 A - cos A cos (C - B) = 0
⇒ cos A [cos A - cos (C - B)] = 0
⇒ cos A [cos (π - (B + C)) - cos (C - B)] = 0
⇒ -cos A [cos (B + C) + cos (C - B)] = 0
⇒ -2 cos A cos B cos C = 0
⇒ cos A = 0 OR cos B = 0 OR cos C = 0
⇒A=ORB=ORC= ∴ The triangle is right-angled.