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

Решите задачу:

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

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