Question

Решите систему уравнений
х+у=pi/2
cos2y+cosx=1

Answer 1

x+y=π/2        x=π/2-y

cos2y+cosx=1

cos²y-sin²y+cos(π/2-y)=sin²y+cos²y

-sin²y+siny=sin²y

2*sin²y-siny=0

siny*(2*siny-1)=0

siny=0

y=0     ⇒     x₁=π/2-0=π/2.

2*sinx-1=0

2*sinx=1  |÷2

siny=1/2

y₂=π/6        ⇒      x₂=π/2-π/6=π/3

y₃=5π/6      ⇒      x₃=π/2-5π/6=-π/3.

Ответ: x₁=π/2     y₁=0      x₂=π/3      y₂=π/6      x₃=-π/3      y₃=5π/6.