Mathematics
语言:中文
Language:English

current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality (((1+sinx)/(1-sinx))-1)/(2*sqrt((1+sinx)/((1-sinx)-1)) ) >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 ) - 1 ) ) ) > tan x         (1)
        From the definition field of divisor
         1 - sin x ≠ 0        (2 )
        From the definition field of divisor
         ( 1 - sin x ) - 1 ≠ 0        (3 )
        From the definition field of √
         ( 1 + sin x ) / ( ( 1 - sin x ) - 1 ) ≥ 0        (4 )
        From the definition field of divisor
         2 * sqrt ( ( 1 + sin x ) / ( ( 1 - sin x ) - 1 ) ) ≠ 0        (5 )

    From inequality(1):
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!
    From inequality(2):
         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(3):
         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(4):
         x ≤ -3926991/500000 或  -3926991/500000 ≤ x ≤ -6.283185 或  -3.141593 ≤ x ≤ -1570797/1000000 或  -1570797/1000000 ≤ x ≤ -1570797/1000000 或  -1570797/1000000 ≤ x ≤ 0 或  3.141593 ≤ x ≤ 4712389/1000000 或  4712389/1000000 ≤ x ≤ 4712389/1000000 或  4712389/1000000 ≤ x ≤ 6.283185
    From inequality(5):
         x < -7.853982 或  -7.853982 < x < -3.141593 或  -3.141593 < x < -1.570797 或  -1.570797 < x < 3.141593 或  3.141593 < x < 4.712389 或  4.712389 < x < 9.424778 或  9.424778 < x < 10.995574 或  x > 10.995574

    From inequalities (1) and (2)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (6)
    From inequalities (3) and (6)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (7)
    From inequalities (4) and (7)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (8)
    From inequalities (5) and (8)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (9)

    The final solution set is :

        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!

    *Note: Radian.



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


Return