In which of the following intervals the inequality, `sinx < cos x < tanx < cot x` can hold good ? (a) `((7pi)/4,2pi)` (b) `((3pi)/4,pi)` (c) `((5pi)/4,(3pi)/2)` (d) `(0,(pi)/4)`

Options

A. `((7pi)/4,2pi)`
B. `((3pi)/4,pi)`
C. `((5pi)/4,(3pi)/2)`
D. `(0,(pi)/4)`

Answer

D

Explanation

In the second quadrant, `sinxltcosx` is false, as sinx is positive and cosx is negative.
In the third quadrant, i.e., `((5pi)/4,(3pi)/2)` is tanx lt cotx then `tan^2xlt1`, which is false.
Now,`sinxltcosx" is true in "(0,pi/4)` and tanxltcotx is also true.
Further, cosx lt cotx, as `cotx=cosx/sinx and sinxlt1`.