THE MIN VALUE OF 2sinx+2cosx is?

Dear vardaan

2^sinx+2^cosx 

use AM ≥GM

 (2^sinx+2^cosx )/2 ≥(2^sinx2^cosx )^1/2

(2^sinx+2^cosx ) ≥2(2^sinx+cosx)^1/2

(2^sinx+2^cosx ) ≥2*2^{(sinx+cosx)/2}

(2^sinx+2^cosx ) ≥2*2^{sin(x+45)/√2}

(2^sinx+2^cosx ) ≥2*2^-1/√2

2^sinx+2^cosx  ≥2^{1 -1/√2}

   
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