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 ln((sinx+lnx+e3)/cosx) >0 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         ln ( ( sin x + ln x + e 3 ) / cos x ) >0         (1)
        From the definition field of ln
        x > 0        (2 )
        From the definition field of ln
         ( sin x + ln x + e 3 ) / cos x > 0        (3 )

    From inequality(1):
         4.712389 < x < 10.995574 或  10.995574 < x < 17.27876 或  17.27876 < x < 23.561945 或  23.561945 < x < 29.84513 或  29.84513 < x < 36.128316 或  36.128316 < x < 42.411501 或  42.411501 < x < 48.694686 或  48.694686 < x < 54.977871 或  x > 54.977871
    From inequality(2):
         x > 0
    From inequality(3):
         0 < x < 1.570796 或  4.712389 < x < 7.853982 或  10.995574 < x < 14.137167 或  17.27876 < x < 20.420352 或  23.561945 < x < 26.703538

    From inequalities (1) and (2)
         4.712389 < x < 10.995574 或  10.995574 < x < 17.27876 或  17.27876 < x < 23.561945 或  23.561945 < x < 29.84513 或  29.84513 < x < 36.128316 或  36.128316 < x < 42.411501 或  42.411501 < x < 48.694686 或  48.694686 < x < 54.977871 或  x > 54.977871    (4)
    From inequalities (3) and (4)
         4.712389 < x < 7.853982 或  x > 998.579726 或  10.995574 < x < 14.137167 或  4.712389 < x < 10.995574 或  17.27876 < x < 20.420352 或  10.995574 < x < 17.27876 或  23.561945 < x < 26.703538     (5)

    The final solution set is :

         4.712389 < x < 7.853982 或  x > 998.579726 或  10.995574 < x < 14.137167 或  4.712389 < x < 10.995574 或  17.27876 < x < 20.420352 或  10.995574 < x < 17.27876 或  23.561945 < x < 26.703538

    *Note: Radian.



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