In which of the following intervals does the trigonometric inequality sec(x) < cot(x) always hold true.
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The inequality for sec (x) < cot (x) is; π/2 < x < π
We are given that;
We want to find the intervals that the trigonometric inequality sec (x) < cot (x) always hold true.
This can also be expressed as;
1/cos (x) < 1/tan (x)
Now, this can happen only in the quadrant where tan (x) is negative and cos x is positive which is in fourth quadrant where;
π/2 < x < π
The inequality for sec (x) < cot (x) is; π/2 < x < π
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