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The number of solutions of the equation...

The number of solutions of the equation `[y+[y]]=2 cosx, ` where `y=(1)/(3)[sinx+[sinx+[sinx]]]` (where [.] denotes the greatest integer function) is

A

4

B

2

C

3

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
`[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.
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