Question

The function $f\left(x\right)=\frac{{\sin }^{4}x+{\cos }^{4}x}{x+\tan x}$ is

• A. odd
• B. even
• C. neither even nor odd
• D. odd and periodic

Answer 1

The correct option is A odd

We have $f\left(x\right)=\frac{{\sin }^{4}x+{\cos }^{4}x}{x+\tan x}$

$\Rightarrow f(-x)=\frac{{\sin }^{4}x+{\cos }^{4}x}{-x-\tan x}=-f\left(x\right)$

so, $f\left(x\right)$ is an odd function.

Clearly $f\left(x\right)$ is not a periodic because of $x$ term is there in denominator.