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Question

If cos3x+sin(2x7π6)=2, then x is equal to

A
π3(2k+1), kZ
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B
π3(6k1), kZ
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C
π3(6k+1), kZ
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D
None of these
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Solution

The correct option is C π3(6k+1), kZ
cos3x+sin(2x7π6)=2
1+cos3x+1+sin(2x7π6)=0
(1+cos3x)+1cos(2x2π3)=0
2cos23x2+2sin2(xπ3)=0
cos3x2=0 and sin(xπ3)=0
3x2=π2,3π2,
and xπ3=0,π,2π,

Therefore, the general solution is x=2kπ+π3=π3(6k+1), kZ

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