Task/28555810
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Решите тригонометрическое уравнение 2cosx + |cosx|=2sin2x*sin(π/6)
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решение: 2cosx + |cosx|=sin2x * * * sin(π/6) =1/2 * * *
2cosx + |cosx|=2sinxcosx * * * sin2x = 2sinxcosx * * *
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а) cosx < 0
cosx = 2sinxcosx ; * * * |cosx| = - cosx * * *
2cosx(sinx -1/2) = 0 ;
sinx =1/2 ;
x =(π-π/6)+2πk ,k ∈ ℤ
x =5π/6 +2πk ,k ∈ ℤ .
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б) cosx=0
x = π/2 +πn , n ∈ ℤ
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в) cosx >0 * * * |cosx| = - cosx * * *
3cosx = 2sinxcosx ;
2cosx(sinx -3/2) =0 ⇒ x ∈ ∅ . * * * sinx ≠ 3/2 >1 * * *
ответ: 5π/6 +2πk , π/2 +πn k,n ∈ ℤ .