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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality tanx
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities：
tan x < sin x (1)
sin x <100 ^ ln x + 10 ^ ln ( 90 - x ) (2)
From the definition field of ln
x > 0 (3 )
From the definition field of ln
90 - x > 0 (4 )
From inequality(1)：
-7.853982 < x < -1256637/200000 或 -4.712389 < x < -3.141593 或 -1.570796 < x < 0 或 1.570796 < x < 3.141593 或 4.712389 < x < 1256637/200000
From inequality(2)：
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(3)：
x ＞ 0
From inequality(4)：
x < 90
From inequalities (1) and (2)
-7.853982 < x < -1256637/200000 或 -4.712389 < x < -3.141593 或 -1.570796 < x < 0 或 1.570796 < x < 3.141593 或 4.712389 < x < 1256637/200000 (5)
From inequalities (3) and (5)
0 < x < 0 或 1.570796 < x < 3.141593 或 4.712389 < x < 1256637/200000 (6)
From inequalities (4) and (6)
0 < x < 0 或 1.570796 < x < 3.141593 或 4.712389 < x < 1256637/200000 (7)
The final solution set is :
0 < x < 0 或 1.570796 < x < 3.141593 或 4.712389 < x < 1256637/200000 Your problem has not been solved here? Please take a look at the hot problems ！
