Mathematics
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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 log(sinx,cosx) >0 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         log( sin x , cos x ) >0         (1)
        From the definition field of log
         sin x > 0        (2 )
         cos x > 0 also ≠ 1        (3 )

    From inequality(1):
         x > √315827341/√500000
    From inequality(2):
         x < -15.707963 或  -12.566371 < x < -9.424778 或  -6.283185 < x < -3.141593 或  0 < x < 3.141593 或  6.283185 < x < 9.424778 或  x > 12.566371
    From inequality(3):
         -14.137167 < x < -12566371/1000000 或  -12566371/1000000 < x < -10.995574 或  -7.853982 < x < -3141593/500000 或  -3141593/500000 < x < -4.712389 或  -1.570796 < x < 0 或  0 < x < 1.570796 或  4.712389 < x < 1256637/200000 或  1256637/200000 < x < 7.853982 或  10.995574 < x < 1256637/100000 或  1256637/100000 < x < 14.137167

    From inequalities (1) and (2)
         x > √315827341/√500000    (4)
    From inequalities (3) and (4)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (5)

    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.



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