Question

Помогите решить
$cos ^{2} (x) + sin(x) = sqrt{2} times sin(x + pi div 4)$

Answer 1

$cos^2x+sin x=sqrt{2}times sin(x+frac{pi}{4})\ cos^2x+sin x=sqrt{2}times (sin xcosfrac{pi}{4}+cos xsinfrac{pi}{4})\ cos^2x+sin x=sqrt{2}times(frac{1}{sqrt{2}}sin x+frac{1}{sqrt{2}}cos x)\ cos^2x+sin x=sin x+cos x\ cos^2x-cos x=0\ cos x(cos x-1)=0\ x_1=frac{pi}{2}+pi n,n in Z\ x_2=2pi n,n in Z$