take the deritiivive
\(ln(2)cos(x)2^{sin(x)}-ln(2)sin(x)2^{cos(x)}\)
it is zero at pi/4 and it repeats at every pi
minimum at where slope goesfrom negative to positive
so at 5pi/4 and 13pi/4 so at every 2pi interval
evaluate origial at 5pi/4
\(2^{sin(5pi/4)}+2^{cos(5pi/4)}\)=
\((2^ \frac{- \sqrt{2} }{2} )+(2^ \frac{- \sqrt{2} }{2} )\)=
\(2(2^ \frac{- \sqrt{2} }{2} )\) or aprox 1.22509
