First slide

Functions (XII)

Question

$What is the fundamental period of f (x) = \frac{\sin x + \sin 3 x}{\cos x + \cos 3 x} ?$

Moderate

A

$\frac{π}{2}$
B

$π$
C

$2 π$
D

$3 π$

Solution

$f (x) = \frac{\sin x + \sin 3 x}{\cos x + \cos 3 x} \Rightarrow f (π + x) = \frac{\sin (π + x) + \sin 3 (π + x)}{\cos (π + x) + \cos 3 (π + x)} = \frac{- \sin x - \sin 3 x}{- \cos x - \cos 3 x} = f (x)$
$T h u s f (x) p e r i o d i s π . (since f (\frac{π}{2} + x) \neq f (x))$

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