Question

How to find result ?

Answer 1

The solution set is the singleton set `{0}`

Explanation:

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

`sin^6x+cos^10x le 1`

and thus

`2x^2 le sin^6x+cos^10x-1 le 0` is only possible if

`x = 0`