find the most general solutions for 2^{sin x} + 2^{cos x} = 2^{1 - (2)-1/2}

Dear

2^{sin x} + 2^{cos x} = 2^{1 - (2)-1/2}

As we know AM ≥GM

                 (2^{sin x} + 2^{cos x})/2≥(2^{sin x}  2^{cos x} )^1/2    equality occur when 2^{sin x} = 2^{cos x}

       or   (2^{sin x} + 2^{cos x})/2≥(2^{sin x +cosx} )^1/2

  mimimum value occur sinx+cosx=-√2

      or   (2^{sin x} + 2^{cos x})/2≥(2^-√2 )^1/2

     or   (2^{sin x} + 2^{cos x})≥2^1-1/√2 

  so for solution equality should be occur

ie   2^{sin x} = 2^{cos x}

   sinx =cosx

 tanx =1

  x=n∏ +∏/4

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