First slide

Compound angles

Question

If $\frac{x}{\cos θ} = \frac{y}{\cos (θ - \frac{2 π}{3})} = \frac{z}{\cos (θ + \frac{2 π}{3})}$ , then $x + y + z =$

Moderate

A

1
B

0
C

-1
D

2

Solution

We have,
$\frac{x}{\cos θ} = \frac{y}{\cos (θ - \frac{2 π}{3})} = \frac{z}{\cos (θ + \frac{2 π}{3})}$
Therefore, each ratio is equal to
$\begin{array}{l} \frac{x + y + z}{\cos θ + \cos (θ - \frac{2}{3} π) + \cos (θ + \frac{2 π}{3})} = \frac{x + y + z}{0} \\ \Rightarrow x + y + z = 0 \end{array}$

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