√2*cos(2x)=cos(x)+sin(x)
(√2*cos(2x))²=(cos(x)+sin(x))²
2*cos²(2x)=cos²(x)+2*sin(x)*cos(x)+sin²(x)
2*(1-sin²(2x))=1+sin(2x)
2-2*sin²(2x)=1+sin(2x)
2*sin²(2x)+sin(2x)-1=0
Пусть sin(2x)=t ⇒
2t²+t-1=0 D=9 √D=3
t₁=sin(2x)=-1 2x=3π/2+2πn x₁=3π/4+πn
t₂=sin(2x)=1/2 2x=π/6+2πn x₂=π/12+πn
2x=5π/6+2πn x₃=5π/12+πn.
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√2*cos(2x)=cos(x)+sin(x)
(√2*cos(2x))²=(cos(x)+sin(x))²
2*cos²(2x)=cos²(x)+2*sin(x)*cos(x)+sin²(x)
2*(1-sin²(2x))=1+sin(2x)
2-2*sin²(2x)=1+sin(2x)
2*sin²(2x)+sin(2x)-1=0
Пусть sin(2x)=t ⇒
2t²+t-1=0 D=9 √D=3
t₁=sin(2x)=-1 2x=3π/2+2πn x₁=3π/4+πn
t₂=sin(2x)=1/2 2x=π/6+2πn x₂=π/12+πn
2x=5π/6+2πn x₃=5π/12+πn.
√2*cos(2x)=cos(x)+sin(x) (√2*cos(2x))²=(cos(x)+sin(x))² 2*cos²(2x)=cos²(x)+2*sin(x)*cos(x)+sin²(x) 2*(1-sin²(2x))=1+sin(2x) 2-2*sin²(2x)=1+sin(2x) 2*sin²(2x)+sin(2x)-1=0 Пусть sin(2x)=t ⇒ 2t²+t-1=0 D=9 √D=3 t₁=sin(2x)=-1 2x=3π/2+2πn x₁=3π/4+πn t₂=sin(2x)=1/2 2x=π/6+2πn x₂=π/12+πn 2x=5π/6+2πn x₃=5π/12+πn