Let $\mathrm{A}={\sin }^{10}\mathrm{\theta }+{\cos }^{14}\mathrm{\theta }$ then for all values of $\theta$ is equal to

$:{\sin }^2\theta \le 1\Rightarrow {\sin }^{10}\theta \le {\sin }^2\theta$
$\begin{array}{l}{\cos }^2\mathrm{\theta }\le 1\Rightarrow {\cos }^{14}\mathrm{\theta }\le {\cos }^2\mathrm{\theta }\\ {\sin }^{10}\mathrm{\theta }+{\cos }^{14}\mathrm{\theta }\le {\sin }^2\mathrm{\theta }+{\cos }^2\mathrm{\theta }=1\end{array}$
Also ${\sin }^{10}\mathrm{\theta }\text{ and }{\cos }^{14}\mathrm{\theta }$ can not be zero simultaneously,
$\text{ Hence, }0<A\le 1\text{. }$