In which one of the following intervals the inequality sinx < cosx < tanx < cotx can hold good?

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$(\frac{7 π}{4}, 2 π)$

$(\frac{3 π}{4}, π)$

$(\frac{5 π}{4}, \frac{3 π}{2})$

$(0, \frac{π}{4})$

answer is D.

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Detailed Solution

In the second quadrant, sinx ( cosx is false, as sinx is positive and cosx is negative.

In the fourth quadrant, cosx <tanx is false, as cosx is positive and tanx is negative.

In the third quadrant, i.e. $(\frac{5 π}{4}, \frac{3 π}{2}) if \tan x < \cot x$ then $\tan^{2} x < 1$ which is false.

Now, sinx < cosx is true in $(0, \frac{π}{4})$ and tanx < cotx is also true,
Further cosx < cotx, as cotx $= \frac{\cos x}{\sin x}$ and sinx < 1.

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