Question

Решите систему уравнений $left { {{x+y= frac{ pi }{2} } atop {cosx-cosy=- sqrt{2} }} right.$ в ответе запишите значение y∈[0; 360]в градусах.

Answer 1

x=π/2-y
cos(π/2-y)-cosy=-√2
-2sin(π/4-y)*sinπ/4=-√2
-2*√2/2*sin(π/4-y)=-√2
sin(π/4-y)=1
cos(π/4+y)=1
π/4+y=2πn
y=-π/4+2πn⇒x=3π/4+2πn
y=7π/4=315гр∈(0;360)