Докажите тождество √2 cos(α+π/4)=cos α-sin α        

[latex] sqrt{2}cos( alpha + frac{ pi }{4} )= sqrt{2}(cos alpha cosfrac{ pi }{4}-sin alpha sinfrac{ pi }{4})=sqrt{2}(cos alpha * frac{ sqrt{2} }{2} -sin alpha * frac{ sqrt{2} }{2} )= sqrt{2}* frac{ sqrt{2} }{2} (cos alpha -sin alpha ) = frac{2}{2}(cos alpha -sin alpha ) =cos alpha -sin alpha[/latex] ч.т.д.