a..certainly I can I can use differential and..but like if I take the 2 numbers in A.P.....then by using A.P.>GP...

\(\displaystyle 2^{sin x}+2^{cos x} >=2^{1-1/sqrt(2)}\)

so I am able to get the minimum value...but is there an algebraic way to solve it...not using calculus...I am rather uncomfortable with calculus if it goes complex.