Question

If 4 cos A cos B + sin 2A + sin 2B + sin 2C = 4 then ∆ABC is

• A. Right angle
• B. Isosceles
• C. Right angled isosceles
• D. None of these

Answer 1

Answer: (C)

Right angled isosceles

Answer 2

Q 4 cos A cos B + 4 sin A sin B sin C = 4

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

⇒ cos (A – B) ≥ 1

⇒ cos (A – B) = 1

True if A = B … (2)

Put (2) in (1)

sin C = 1

C = 90⁰