Question

Решить уравнение sinx+cosx=√2

Answer 1

$sin x + cos x=sqrt{2}$
$sin x*frac{1}{sqrt{2}}+cos x*frac{1}{sqrt{2}}=1$
$sin x cos frac{pi}{4}+cos x*sin frac{pi}{4}=1$
$sin(x+frac{pi}{4})=1$
$x+frac{pi}{4}=frac{pi}{2}+2*pi*k$
$x=frac{pi}{4}+2*pi*k$
k є Z