Докажите тождество.
[tex] \frac{sin \alpha +cos \alpha }{ \sqrt{2} } =cos( \alpha - \frac{ \pi }{4} )[/tex]
[tex] \frac{sin \alpha +cos \alpha }{ \sqrt{2} } =cos( \alpha - \frac{ \pi }{4} )[/tex]
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Cos(a-pi/4)=cos(a)*cos(pi/4)+sin(a)*sin(pi/4)=cos(a)*корень(2)/2+sin(a)*корень(2)/2=(cos(a)+sin(a))/корень(2) - доказано