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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality 2 ≥(1+tanx)(1+tan(45-x)) ≥2 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
2 ≥ ( 1 + tan x ) * ( 1 + tan ( 45 - x ) ) (1)
( 1 + tan x ) * ( 1 + tan ( 45 - x ) ) ≥2 (2)
From inequality(1):
x ≤ -6.836279 或 -4.712389 ≤ x ≤ -3.694686 或 -1.570796 ≤ x ≤ -0.553093 或 1.570796 ≤ x ≤ 2.588499 或 4.712389 ≤ x ≤ 5.730092 或 x ≥ 7.853982
From inequality(2):
-6.836279 ≤ x ≤ -4.712389 或 -3.694686 ≤ x ≤ -1.570796 或 -0.553093 ≤ x ≤ 1.570796 或 2.588499 ≤ x ≤ 4.712389 或 5.730092 ≤ x ≤ 7.853982
From inequalities (1) and (2)
-6.836279 ≤ x ≤ -6.836279 或 -3.694686 ≤ x ≤ -3.694686 或 -0.553093 ≤ x ≤ -0.553093 或 2.588499 ≤ x ≤ 2.588499 或 5.730092 ≤ x ≤ 5.730092 或 7.853982 ≤ x ≤ 7.853982 (3)
The final solution set is :
-6.836279 ≤ x ≤ -6.836279 或 -3.694686 ≤ x ≤ -3.694686 或 -0.553093 ≤ x ≤ -0.553093 或 2.588499 ≤ x ≤ 2.588499 或 5.730092 ≤ x ≤ 5.730092 或 7.853982 ≤ x ≤ 7.853982 *Note: Radian.Your problem has not been solved here? Please take a look at the hot problems !