Question

1/2cos(x/16)+1/2sin(x/16)=?

Answer 1

$frac{1}{2} cos frac{x}{16} + frac{1}{2} sin frac{x}{16} = frac{1}{ sqrt{2} } * sqrt{2} *( frac{1}{2} cos frac{x}{16} + frac{1}{2} sin frac{x}{16})=$$=frac{1}{ sqrt{2} }(frac{ sqrt{2} }{2} cos frac{x}{16} + frac{ sqrt{2} }{2} sin frac{x}{16})= frac{1}{ sqrt{2} }(sinfrac{ pi }{4} cos frac{x}{16} + cosfrac{ pi }{4} sin frac{x}{16})=$ $frac{1}{ sqrt{2} }sin( frac{ pi }{4}- frac{x}{16} )$

$sin(x+y)=sinx*cosy+cosx*siny$