Question

решить систему уравнений:
x+y=пи/2
sinx+siny=- корень из 2

Answer 1

{x+y=π/2⇒y=π/2-x
{sinx+siny=-√2
sinx+sin(π/2-x)=-√2
2sinπ/4*cos(x-π/4)=-√2
2*√2/2*cos(x-π/4)=-√2
cos(x-π/4)=-1
x-π/4=0
x=π/4
y=π/2-π/4=π/4
(π/4;π/4)