First slide

Compound angles

Question

In $a Δ P Q R, ∠ R = \frac{π}{2} . If \tan \frac{P}{2} and \tan \frac{Q}{2}$ are the roots of equation $a x^{2} + b x + c = 0 (a \neq 0)$ , then

Moderate

A

$a + b = c$
B

$b + c = a$
C

$c + a = b$
D

$b = c$

Solution

We have,
$\begin{array}{l} P + Q + R = π and R = \frac{π}{2} \\ ∴ P + Q = \frac{π}{2} \\ \Rightarrow \frac{P}{2} + \frac{Q}{2} = \frac{π}{4} \\ \Rightarrow \tan (\frac{P}{2} + \frac{Q}{2}) = 1 \\ \Rightarrow \tan \frac{P}{2} + \tan \frac{Q}{2} = 1 - \tan \frac{P}{2} \tan \frac{Q}{2} \end{array}$

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