First slide

Extreme values and Periodicity of Trigonometric functions

Question

If $f (x + k) + f (x) = 0 \forall x \in R$ and $k \in R^{+},$ then the period of f(x) is

Moderate

A

0
B

$\frac{π}{2}$
C

2K
D

Does not exist

Solution

$f (x + k) + f (x) = 0$
x is replaced by $x + k$
then we get $f (x + 2 k) + f (x + k) = 0$
$\Rightarrow f (x + 2 k) = - f (x + k)$
$\Rightarrow f (x + 2 k) = f (x)$

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