Question

In a ∆ PQR, ∠ R = $\frac{\pi}{2}$. If tan $\left( \frac{P}{2} \right)$ and tan $\left( \frac{Q}{2} \right)$are the roots of the equation ax² + bx + c = 0 (a ≠ 0), then

• A. a + b = c
• B. b + c = 0
• C. a + c = b
• D. b = c

Answer 1

Answer: (A)

a + b = c

Answer 2

$\frac{P}{2}$+ $\frac{Q}{2}$= $\frac{\pi}{4}$

∴ tan $\left( \frac{P}{2} + \frac{Q}{2} \right)$= tan $\frac{\pi}{4}$⇒$\frac{\tan\frac{P}{2} + \tan\frac{Q}{2}}{1 - \tan\frac{P}{2}\tan\frac{Q}{2}}$= 1

$\frac{\frac{- b}{a}}{1 - \frac{c}{a}}$= 1 ⇒ a + b = c