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The number of solutions of the equation ...

The number of solutions of the equation `tan^(-1)(4{x})+cot^(-1)(x+[x]))=(pi)/(2)` is (where `[.]` denotes greatest integer function and `{.}` fractional part of function.

A

3

B

2

C

1

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
`because4{x}=x+[x]` . . .(1)
case 1 let `x=I`
`O=I+IimpliesI=0`
Case 2 let `x=I+F,0ltflt1`
`therefore` equation (1) becomes
`4f=I+f+I`
`f+(2I)/(3)`
`thereforeI=1,f=(2)/(3)thereforer=(5)/(3)`
`therefore` two solutions
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