First slide

Compound angles

Question

If tan x + tan 2x + tan 3x = tan x tan 2x tan 3x, then value $| \sin 3 x + \cos 3 x |$ is _____ .

Moderate

Solution

$\begin{array}{l} \tan x + \tan 2 x + \tan 3 x = \tan xtan 2 xtan 3 x \\ \Rightarrow x + 2 x + 3 x = nπ, n \in Z \\ \Rightarrow x = nπ / 6, n \in Z \\ ∴ | \sin 3 x + \cos 3 x | = 1 \end{array}$

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