Question

If A, B, and C are the angles of a triangle such that angle A is obtuse, then tan B tan C will be less than

• A. $\frac{1}{\sqrt{3}}$
• B. $\frac{\sqrt{3}}{2}$
• C. 1
• D. None of these

Answer 1

Answer: (C)

1

Answer 2

Since A is obtuse angle, 90⁰ < A < 180⁰

⇒ 90⁰ < 180 – (B + C) < 180⁰

⇒ – 90⁰ > B + C – 180⁰ > –180⁰

⇒ 90⁰ > B + C > 0

⇒ B + C < 90⁰ ⇒ B < 90⁰ – C

⇒ tan B < tan (90⁰ – C) ⇒ tan B < cot C

⇒ tan B tan C < 1