First slide

Trigonometric transformations

Question

If $\cos A + \cos B + \cos C = 0$ then $\cos 3 A + \cos 3 B + \cos 3 C = λ \cos A \cos B \cos C$ then $λ =$

Moderate

A

12
B

14
C

16
D

15

Solution

$\cos A + \cos B + \cos C = 0$
$\Rightarrow \cos^{3} A + \cos^{3} B + \cos^{3} C$
$= 3 \cos A \cos B \cos C$ and $\cos 3 A + \cos 3 B + \cos 3 C$
$= 4 (\cos^{3} A + \cos^{3} B + \cos^{3} C) - 3 (\cos A + \cos B + \cos C)$
$= 4 (3 \cos A \cos B \cos C) - 3 (0)$
$= 12 \cos a \cos B \cos C$

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