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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality 1.99 <(1+tanx)(1+tan(45-x)) <2.01 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
1.99 < ( 1 + tan x ) * ( 1 + tan ( 45 - x ) ) (1)
( 1 + tan x ) * ( 1 + tan ( 45 - x ) ) <2.01 (2)
From inequality(1):
-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 inequality(2):
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 inequalities (1) and (2)
或 x < -6.836279 或 -4.712389 < x < -3.694686 或 -1.570796 < x < -0.553093 (3)
The final solution set is :
或 x < -6.836279 或 -4.712389 < x < -3.694686 或 -1.570796 < x < -0.553093 *Note: Radian.Your problem has not been solved here? Please take a look at the hot problems !