Using $A.M. \ge G.M.$,
$\frac{{{e^x} + {e^{ – x}}}}{2} \ge \sqrt {{e^x}.{e^{ – x}}} $
$ \Rightarrow {e^x} + {e^{ – x}} \ge 2$
$\therefore \sin ({\pi ^x}) \ge 2$ which is not possible for any real x.
So, no solution.
Using $A.M. \ge G.M.$,
$\frac{{{e^x} + {e^{ – x}}}}{2} \ge \sqrt {{e^x}.{e^{ – x}}} $
$ \Rightarrow {e^x} + {e^{ – x}} \ge 2$
$\therefore \sin ({\pi ^x}) \ge 2$ which is not possible for any real x.
So, no solution.