First slide

Multiple and sub- multiple Angles

Question

If $θ_{1} and θ_{2}$ are two values lying in $[0, 2 π]$ for which $\tan θ = λ, then \tan \frac{θ_{1}}{2} \tan \frac{θ_{2}}{2}$ is equal to

Moderate

A

0
B

-1
C

2
D

1

Solution

$\tan θ = λ$ we get $\frac{2 \tan θ / 2}{1 - \tan^{2} θ / 2} = λ$
$\begin{array}{l} or {λtan}^{2} \frac{θ}{2} + 2 \tan \frac{θ}{2} - λ = 0 \\ \Rightarrow \tan \frac{θ_{1}}{2} \tan \frac{θ_{2}}{2} = - 1 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App