Let `f(x)=[t a n x[cot x]],x [pi/(12),pi/(12)]` , (where [.] denotes the greatest integer less than or equal to`x` ). Then the number of points, where `f(x)` is discontinuous is a. one b. zero`` c. three d. infinite

Options

A. one
B. zero
C. three
D. infinite

Answer

C

Explanation

We `x in I`.
`rArr" "tanx[cotx]=1`
`rArr" "[tanx[cotx]lt1`
When, `x in I`,
`[cotx]ltcotx`
`rArr" "0 lt tanx[cotx]lt1`
`rArr" "[tanx[cotx]]=0`
`rArr" "f(x)=[tanx[cotx]]={{:(1",",cotx in I),(0",",cot x cancelinI):}`
So, f(x) is discontinuous when `cot x in I`
Now `(pi)/(12)le x lt(pi)/(2)`
`rArr" "0 lt cot x le2+sqrt3`
Hence, number of points of discontinuity are `x=cot^(-1)3, cot^(-1)2` and `cot^(-1)1=(pi)/(4)`.
Thus three points of discontinuity.