How to find result ?

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How to find result ?

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Answer 1 · 2018-03-29T09:33:22

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

Explanation:

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

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

and thus

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

$x = 0$ $x = 0$

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