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           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality 2tanA/(1+3tanA^2) <= 1/sqrt(3) .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
        2 * tan A / ( 1 + 3 * tan A ^ 2 ) <= 1 / sqrt ( 3 )         (1)
        From the definition field of divisor
         1 + 3 * tan x ^ 2 ≠ 0        (2 )

    From inequality(1):
         A ≤ -8901179/1000000 或  -8901179/1000000 ≤ A ≤ -5759587/1000000 或  -5759587/1000000 ≤ A ≤ -5759587/1000000 或  -5759587/1000000 ≤ A ≤ -1308997/500000 或  -1308997/500000 ≤ A ≤ -1308997/500000 或  -1308997/500000 ≤ A ≤ 523599/1000000 或  523599/1000000 ≤ A ≤ 523599/1000000 或  523599/1000000 ≤ A ≤ 458149/125000 或  458149/125000 ≤ A ≤ 458149/125000 或  458149/125000 ≤ A ≤ 106356/15625 或  A ≥ 106356/15625
    From inequality(2):
         A ∈ R (R为全体实数),即在实数范围内,不等式恒成立!

    From inequalities (1) and (2)
         A ≤ -8901179/1000000 或  -8901179/1000000 ≤ A ≤ -5759587/1000000 或  -5759587/1000000 ≤ A ≤ -5759587/1000000 或  -5759587/1000000 ≤ A ≤ -1308997/500000 或  -1308997/500000 ≤ A ≤ -1308997/500000 或  -1308997/500000 ≤ A ≤ 523599/1000000 或  523599/1000000 ≤ A ≤ 523599/1000000 或  523599/1000000 ≤ A ≤ 458149/125000 或  458149/125000 ≤ A ≤ 458149/125000 或  458149/125000 ≤ A ≤ 106356/15625 或  A ≥ 106356/15625    (3)

    The final solution set is :

         A ≤ -8901179/1000000 或  -8901179/1000000 ≤ A ≤ -5759587/1000000 或  -5759587/1000000 ≤ A ≤ -5759587/1000000 或  -5759587/1000000 ≤ A ≤ -1308997/500000 或  -1308997/500000 ≤ A ≤ -1308997/500000 或  -1308997/500000 ≤ A ≤ 523599/1000000 或  523599/1000000 ≤ A ≤ 523599/1000000 或  523599/1000000 ≤ A ≤ 458149/125000 或  458149/125000 ≤ A ≤ 458149/125000 或  458149/125000 ≤ A ≤ 106356/15625 或  A ≥ 106356/15625

    *Note: Radian.



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