Number of solutions of the equation, `[y+[y]]=2cosx` is: (where `y=(1//3)[sinx+[sinx+[sinx]]]` and `[]=` greatest integer function) 0 (b) 1 (c) 2 (d) `oo`

Options

A. 4
B. 2
C. 3
D. 0

Answer

D

Explanation

`[y+[y]]=2cos x`
`or [y] +[y]=2cosx " " ( :' [x+n] =[x] + n " if " n in I)`
` or 2[y]=2cosx or [y] =cosx " (1)" `
Also, `y=(1)/(3)[sinx+[sinx+[sinx]]]`
`=(1)/(3)(3[sinx])`
`=[sinx] " (2)" `
From (1) and (2),
`[[sinx]]=cosx`
` or [sinx]=cosx`

The number of solutions is 0.