Решить уравнение
1.
sin2x/3 =1 ;
2x/3 = π/2 +2πn , n ∈Z || *3/2
x = 3π/4 +3πn , n ∈Z .
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2.
tg(4x+π/4) = -√3 ;
4x+π/4 = - π/3 +πn , n ∈Z
4x = - π/3 -π/4 +πn , n ∈Z
x = - 7π/48 +πn/4 , n ∈Z
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3.
2cos(x/2 -π/6) = -√2 ;
cos(x/2 -π/6) = -√2 /2 ;
x/2 -π/6 = ± (π-π/4) +2πn , n∈Z ;
x/2 -π/6 = ± 3π/4 +2πn , n∈Z ;
x = π/3± 3π/2 +4πn , n∈Z ;
x = π/3± 3π/2 +4πn , n∈Z ;
x₁ = 11π/6 +4πn , n∈Z ;
x₂= -7π/6 +4πn , n∈Z .
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4.
2cos²x +7cosx - 4 =0 ; квадратное уравнение относительно cosx
D =7² -4*2*(-4) =49+32 =81 = 9²
cosx = (-7 -9)/2*2 = - 4 < -1 не имеет решения ;
cosx = (-7 +9)/2*2 = 1/2 ;
x = ± π/3 +2πn , n∈Z .