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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality sinx/(cosx)^2+sinx-2x >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sin x / ( cos x ) ^ 2 + sin x - 2 * x >0 (1)
From the definition field of divisor
cos x ≠ 0 (2 )
From inequality(1):
x < -14.326691 或 -13.944991 < x < -8.10864 或 -7.59033 < x < -2.10314 或 0 < x < 2.10314 或 7.59033 < x < 8.10864 或 x > 13.944991
From inequality(2):
x < -14.137167 或 -14.137167 < x < -10.995574 或 -10.995574 < x < -7.853982 或 -7.853982 < x < -4.712389 或 -4.712389 < x < -1.570796 或 -1.570796 < x < 1.570796 或 1.570796 < x < 4.712389 或 4.712389 < x < 7.853982 或 7.853982 < x < 10.995574 或 10.995574 < x < 14.137167 或 x > 14.137167
From inequalities (1) and (2)
x < -14.326691 或 -13.944991 < x < -10.995574 或 -10.995574 < x < -8.10864 或 x < -14.137167 或 -7.59033 < x < -4.712389 或 -4.712389 < x < -2.10314 或 0 < x < 1.570796 或 1.570796 < x < 2.10314 或 7.59033 < x < 7.853982 或 7.853982 < x < 8.10864 或 13.944991 < x < 14.137167 或 x > 14.137167 (3)
The final solution set is :
x < -14.326691 或 -13.944991 < x < -10.995574 或 -10.995574 < x < -8.10864 或 x < -14.137167 或 -7.59033 < x < -4.712389 或 -4.712389 < x < -2.10314 或 0 < x < 1.570796 或 1.570796 < x < 2.10314 或 7.59033 < x < 7.853982 或 7.853982 < x < 8.10864 或 13.944991 < x < 14.137167 或 x > 14.137167 *Note: Radian.Your problem has not been solved here? Please take a look at the hot problems !