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Assignment:Find the solution set of inequality (((1+sinx)/((1-sinx)-1)/(2*sqrt((1+sinx)/((1-sinx))) ) ) ) >tanx .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality：
( ( ( 1 + sin x ) / ( ( 1 - sin x ) - 1 ) / ( 2 * sqrt ( ( 1 + sin x ) / ( ( 1 - sin x ) ) ) ) ) ) > tan x (1)
From the definition field of divisor
( 1 - sin x ) - 1 ≠ 0 (2 )
From the definition field of divisor
( 1 - sin x ) ≠ 0 (3 )
From the definition field of √
( 1 + sin x ) / ( ( 1 - sin x ) ) ≥ 0 (4 )
From the definition field of divisor
2 * sqrt ( ( 1 + sin x ) / ( ( 1 - sin x ) ) ) ≠ 0 (5 )
From inequality(1)：
-4.712389 < x < -3.757072 或 -3.141593 < x < -2.526113 或 -1.570796 < x < 0 或 1.570796 < x < 2.526113 或 3.141593 < x < 3.757072
From inequality(2)：
x < -15.707963 或 -15.707963 < x < -12.566371 或 -12.566371 < x < -9.424778 或 -9.424778 < x < -6.283185 或 -6.283185 < x < -3.141593 或 -3.141593 < x < 0 或 0 < x < 3.141593 或 3.141593 < x < 6.283185 或 6.283185 < x < 9.424778 或 9.424778 < x < 12.566371 或 x ＞ 12.566371
From inequality(3)：
x < -431969/25000 或 -431969/25000 < x < -439823/40000 或 -439823/40000 < x < -4712389/1000000 或 -4712389/1000000 < x < 1570797/1000000 或 1570797/1000000 < x < 3926991/500000 或 3926991/500000 < x < 7068583/500000 或 x ＞ 7068583/500000
From inequality(4)：
x ≤ -14137167/1000000 或 -14137167/1000000 ≤ x ≤ -3926991/500000 或 -3926991/500000 ≤ x ≤ -3926991/500000 或 -3926991/500000 ≤ x ≤ -1570797/1000000 或 -1570797/1000000 ≤ x ≤ -1570797/1000000 或 -1570797/1000000 ≤ x ≤ 4712389/1000000 或 4712389/1000000 ≤ x ≤ 4712389/1000000 或 4712389/1000000 ≤ x ≤ 5497787/500000 或 5497787/500000 ≤ x ≤ 5497787/500000 或 5497787/500000 ≤ x ≤ 17278759/1000000 或 x ≥ 17278759/1000000
From inequality(5)：
x < -14.137167 或 -14.137167 < x < -7.853982 或 -7.853982 < x < -1.570797 或 -1.570797 < x < 4.712389 或 4.712389 < x < 10.995574 或 10.995574 < x < 17.278759 或 x ＞ 17.278759
From inequalities (1) and (2)
或 x < -15.707963 或 -15.707963 < x < -12.566371 或 -4.712389 < x < -3.757072 或 -9.424778 < x < -6.283185 或 -3.141593 < x < -2.526113 或 -1.570796 < x < 0 或 1.570796 < x < 2.526113 或 -1.570796 < x < 0 或 3.141593 < x < 3.757072 (6)
From inequalities (3) and (6)
x < -431969/25000 或 -431969/25000 < x < -15.707963 或 -15.707963 < x < -12.566371 或 -4.712389 < x < -3.757072 或 6.283185 < x < 9.424778 或 -3.141593 < x < -2.526113 或 -1.570796 < x < 0 或 1.570796 < x < 1570797/1000000 或 1570797/1000000 < x < 2.526113 或 x < -15.707963 或 3.141593 < x < 3.757072 (7)
From inequalities (4) and (7)
x < -431969/25000 或 -431969/25000 < x < -15.707963 或 -15.707963 < x ≤ -14137167/1000000 或 -14137167/1000000 ≤ x < -12.566371 或 -4.712389 < x < -3.757072 或 6.283185 < x < 9.424778 (8)
From inequalities (5) and (8)
x < -431969/25000 或 -431969/25000 < x < -15.707963 或 -15.707963 < x < -14.137167 或 -14.137167 < x < -12.566371 或 -4.712389 < x < -3.757072 或 6.283185 < x < 9.424778 (9)
The final solution set is :
x < -431969/25000 或 -431969/25000 < x < -15.707963 或 -15.707963 < x < -14.137167 或 -14.137167 < x < -12.566371 或 -4.712389 < x < -3.757072 或 6.283185 < x < 9.424778 *Note: Radian.Your problem has not been solved here? Please take a look at the hot problems ！
