Given x + sin y = 2009 and x + 2009 cos ...

Given x + sin y = 2009 and x + 2009 cos y = 2008, where `y in[0,(pi)/(2)]`, then [x+y] equals, where [.] represents the greatest integer function,

A

2008

B

2009

C

2100

D

2010

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The correct Answer is:

B

Subtracting we get, sin y = 1 + 2009 cos y
`therefore` Equation is possible if cos y = 0
`therefore y = pi//2` and x = 2008
`therefore [x + y]=2009`

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