Question

In a triangle ABC, cos A cos B + sin A sin B sin C = 1, then the triangle is –

• A. Equilateral
• B. Right angled isosceles
• C. Obtuse angled isosceles
• D. None of these

Answer 1

Answer: (B)

Right angled isosceles

Answer 2

sin C = $\frac { 1 - \cos A \cos B } { \sin A \sin B }$ ≤ 1

⇒ 1 – cos A cos B – sin A sin B ≤ 0

⇒ 1 – cos (A – B) ≤ 0

⇒ cos (A – B) ≥ 1

⇒ cos (A – B) = 1 Q –1 ≤ cos θ ≤ 1

⇒ A – B = 0

⇒ A = B

∴ sin C = ⇒ C = π/2

∴ A = B = π/4

Right Angle Isosceles triangle