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[ 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.Your problem has not been solved here? Please take a look at the hot problems !