Question

In a triangle PQR, $\angle$R = p/2. If tan(P/2) and tan(Q/2) are the roots of the equation ax² + bx + c = 0 where a $\neq$0 then –

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

Answer 1

Answer: (A)

a + b = c

Answer 2

As tan(P/2) & tan(Q/2) roots of ax² + bx + c = 0

We have tan $\left( \frac{P}{2} \right)$ + tan$\left( \frac{Q}{2} \right)$ = $\frac{- b}{a}$ ……(i)

tan $\left( \frac{P}{2} \right)$. tan$\left( \frac{Q}{2} \right)$ = $\frac{c}{a}$ ……….(ii)

also $\angle$R = p/2 then $\angle$P + $\angle$Q = p/2

P + Q = p/2

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

Žtan$\left( \frac{P}{2} + \frac{Q}{2} \right)$= tan$\frac{\pi}{4}$

Ž$\frac{\tan\left( \frac{P}{2} \right) + \tan\left( \frac{Q}{2} \right)}{1 - \tan\left( \frac{P}{2} \right)\tan\left( \frac{Q}{2} \right)}$= 1

Ž$\frac{- \frac{b}{a}}{1 - \frac{c}{a}}$= 1

Ž – b = a – c

Ž a + b = c