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Question

If [sinx]+[2cosx]=3, x[0,2π], (where [.] represents the greatest integer function), then the range of x is 
  1. (5π4,7π4)
  2. (3π4,5π4)
  3. (π,5π4)
  4. (π4,7π4)


Solution

The correct option is C (π,5π4)
[sinx]+[2cosx]=3
We know that, 
sinx[1,1][sinx]{1,0,1}2cosx[2,2][2cosx]{2,1,0,1}
So, solution is possible only when 
[sinx]=1,[2cosx]=21sinx<0x(π,2π)(1)[2cosx]=222cosx<11cosx<12x(3π4,5π4)(2)

From equation (1) and (2), we get
x(π,5π4)

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