# How to find result ?

##### 1 Answer
Mar 29, 2018

The solution set is the singleton set $\left\{0\right\}$

#### Explanation:

Since ${\sin}^{2} x + {\cos}^{2} x = 1$ , ${\sin}^{6} x \le {\sin}^{2} x$ and ${\cos}^{10} x \le {\cos}^{2} x$ (the last two following from the fact that both ${\sin}^{2} x$ and ${\cos}^{2} x$ are bounded above by 1, we have

${\sin}^{6} x + {\cos}^{10} x \le 1$

and thus

$2 {x}^{2} \le {\sin}^{6} x + {\cos}^{10} x - 1 \le 0$ is only possible if

$x = 0$