First slide

Trigonometric Identities

Question

x = y cos $(\frac{4 π}{3}) = z \cos (\frac{8 π}{3}) t h e n$ xy + yz + zx =

Easy

A

1
B

-1
C

$\frac{1}{2}$
D

0

Solution

$\begin{matrix} x = y \cos (\frac{4 π}{3}) = z \cos (\frac{8 π}{3}) \Rightarrow x = \frac{- y}{2} = \frac{- z}{2} = k \\ x y + y z + z x = k (- 2 k) + (- 2 k) (- 2 k) + (- 2 k) k = 0 \end{matrix}$

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