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Question

limxk(x[x]), where k is an integer, is equal to (where [] denotes greatest integer function).

A
1
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B
0
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C
1
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D
Does not exist
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Solution

The correct option is D Does not exist
sinα+sin(α+2π3)+sin(α+4π3)=L
L=sinα+2sin(2α+7π2)cos⎜ ⎜ ⎜4π3+αα2π32⎟ ⎟ ⎟
L=sinα+2sin(α+π)cosπ3
L=sinα+2(sinα)×12
L=0
sina+sinb=2sina+b2cosab2
sin(α+π)=sina
Hence:-
sinα+sin(α+2π3)+sin(α+4π3)=0

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