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.
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.