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Question

Solve sin4(x/3)+cos4(x/3)>1/2.

A
R{x:x=3nπ2±3π4,nϵz}
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B
R{x:x=nπ±3π4,nϵz}
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C
R{x:x=2nπ±3π4,nϵz}
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D
R{x:x=nπ2±3π4,nϵz}
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Solution

The correct option is A R{x:x=3nπ2±3π4,nϵz}
sin4(x3)+cos4(x3)>12
1+2sin2(x3)cos2(x3)>12
12sin2(2x3)>12
sin2(2x3)>1
R(x:x=3nπ2±3π4)

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