First slide

Trigonometric transformations

Question

If $\cos x + \cos y + \cos α = 0$ and $\sin x + \sin y + \sin α = 0$ then $\cot (\frac{x + y}{2})$ is equal to

Moderate

A

sin $α$
B

cos $α$
C

cot $α$
D

$\sin (\frac{x + y}{2})$

Solution

Given equations may be written as
$\begin{array}{l} \cos x + \cos y = - \cos α \\ and \sin x + \sin y = - \sin α \\ \Rightarrow 2 \cos (\frac{x + y}{2}) \cos (\frac{x - y}{2}) = - \cos α - - - - (i) \\ and 2 \sin (\frac{x + y}{2}) \cos (\frac{x - y}{2}) = - \sin α - - - - (ii) \end{array}$
From Eqs. (i) and (ii), we get
$\begin{array}{l} \frac{2 \cos (\frac{x + y}{2}) \cos (\frac{x - y}{2})}{2 \sin (\frac{x + y}{2}) \cos (\frac{x - y}{2})} = \frac{\cos α}{\sin α} \\ \Rightarrow \cot (\frac{x + y}{2}) = \cot α \end{array}$

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