Question 1062122
-sqrt(3) - 1/2 sqrt(3) cos(2 x) + 1/2 sin(2 x) + sqrt(3) (1/2 cos(2 x) + 1/2 sqrt(3) sin(2 x)) = 0
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Simplify and substitute y = 1/2 sin(2 x)
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-sqrt(3) - 1/2 sqrt(3) cos(2 x) + 1/2 sin(2 x) + sqrt(3) (1/2 cos(2 x) + 1/2 sqrt(3) sin(2 x)) = (4 sin(2 x))/2 - sqrt(3) = 4y - sqrt(3) = 0
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4y - sqrt(3) = 0
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Add sqrt(3) to both sides
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4y = sqrt(3)
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Divide both sides by 4
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y = sqrt(3)/4
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Substitute back for y = 1/2 sin(2 x)
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1/2 sin(2x) = sqrt(3)/4
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Multiply both sides by 2
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sin(2x) = sqrt(3)/2
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Take the inverse sine of both sides
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2x = (2π)/3 + 2πn1 for n1 in Z
or 2x = π/3 + 2πn2 for n2 in Z
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Simplify each equation
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Divide both sides by 2
:
x = π/3 + πn1 for n1 in Z
or 2x = π/3 + 2πn2 for n2 in Z
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Divide both sides by 2
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x = π/3 + πn1 for n1 in Z
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or x = π/6 + πn2 for n2 in Z
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