Given the following inequality:
$$\left(\cos(x^x)-\cos(x^y)\right)+\left(\cos(y^y)-\cos(y^x)\right)\gt0$$ how is it possible to find the values of $x,y$ for which the inequality is valid? Thanks
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The following inequality maybe useful $x^y+y^x>1$ – Albus Dumbledore Jan 22 '21 at 14:11
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The solutions are symmetric. If $(a,b)$ is a solution, then $(b,a)$ is a solution, too, provided that $a\ne b$ – Raffaele Jan 22 '21 at 14:34
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Its a continuous map, so find where $\cos x^x + \cos y^y = \cos x^y + \cos y^x$. Points on one side of this curve will satisfy the inequality, while points on the other side will not. – Paul Sinclair Jan 23 '21 at 00:43