Решите уравнение
cos [tex] \frac{x}{3} [/tex] sin [tex] \frac{x}{3} [/tex] = [tex] \frac{1}{4} [/tex]
cos [tex] \frac{x}{3} [/tex] sin [tex] \frac{x}{3} [/tex] = [tex] \frac{1}{4} [/tex]
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Verified answer
Cos(x/3)sin(x/3) = 1/42cos(x/3)sin(x/3) = 1/2
sin(2x/3) = 1/2
2x/3 = (-1)ⁿπ/6 + πn, n ∈ Z
2x = (-1)ⁿπ/2 + 3πn, n ∈ Z
x = (-1)ⁿπ/4 + 3πn/2, n ∈ Z
Ответ: x = (-1)ⁿπ/4 + 3πn/2, n ∈ Z.
Verified answer
task/25490895-------------------
Решите уравнение cos(x/3)* sin(x/3) = 1/4 ;
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* * * sin2α =2sinαcosα * * *
2sin(x/3)*cos(x/3) = 2*1/4 ;
sin(2x/3) = 1/2 ;
2x/3 = (-1)^n * π/6 +πn , n ∈ Z .
x = (-1)^n * π/4 +(3π/2)*n , n ∈ Z .
ответ: (-1)^n * π/4 +(3π/2)*n , n ∈ Z .