Question

If A, B and C are angles of 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: (A)

$\frac { 1 } { \sqrt { 3 } }$

Answer 2

A is obtuse angle then 90⁰ < A < 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.