Question

√2/2sinx-√2/2cosx=1

решите уравнение. 

Answer 1

$frac{sqrt2}{2}cdotsin x-frac{sqrt2}{2}cdotcos x=-1;\ (frac{sqrt2}{2})^2+(frac{sqrt2}{2})^2=frac{2}{4}+frac24=frac44=1;\ sinfracpi4=cosfracpi4=frac{sqrt2}{2};\ 1) sinfracpi4sin x-cosfracpi4cos x=-1;\ -cos(x+fracpi4)=-1;\ cos(x+fracpi4)=1;\ x+fracpi4=2pin;\ x=-fracpi4+2pi n, nin Z;\ 2)cosfracpi4sin x-cos xsinfracpi4=-1;\ sin(x-fracpi4)=-1;\ x-fracpi4=-fracpi2+2pi n, nin Z;\ x=-fracpi2+fracpi4+2pi n, nin Z;$
$x=-fracpi4+2pi n, nin Z$

ответ:
$x=-fracpi4+2pi n, nin Z$