Question

If in a ∆ABC,$\frac{2cosA}{a} + \frac{cosB}{b} + \frac{2cosC}{c} = \frac{a}{bc} + \frac{b}{ac}$, then angle A

equals to

• A. 90⁰
• B. 45⁰
• C. 135⁰
• D. None of these

Answer 1

Answer: (A)

90⁰

Answer 2

We have $\frac{2\cos A}{a} + \frac{\cos B}{b} + \frac{2\cos C}{c} = \frac{a}{bc} + \frac{b}{ac}$

Multiplying

both sides by abc

⇒ 2bc cosA + ac cosB + 2ab cosC = a² + b² (b² + c² – a²) + $\frac{\left( c^{2} + a^{2} - b^{2} \right)}{2} + \left( a^{2} \right)$

⇒ (c² + a² – b²) = 2a² – 2b²

⇒ b² + c² = a² ⇒ ∠A = 90⁰