Question

Determine whether the given function is even or odd ${\sin }^{5}x+2{\tan }^{3}x$

Answer 1

$f\left(x\right)={\sin }^{5}x+2{\tan }^{3}x$

$f\left(x\right)={\sin }^5(-x)+2{\tan }^3(-x)$
$f(-x)=-({\sin }^{5}x+2{\tan }^{3}x)$ (Since, sine and tangent both are odd functions.)

$\Rightarrow f(-x)=-f\left(x\right)$
Therefore, $f\left(x\right)$ is odd.