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Question

The solution of trignometric equation
cos4x+sin4x=2cos(2x+π)cos(2x+π) is

A
x=nπ2±sin1(15)
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B
x=nπ4+(1)n4sin1(15)
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C
x=nπ4+cos1(15)
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D
x=nπ4+(1)n4cos1(15)
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E
None of the above
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Solution

The correct option is E None of the above
Given cos4x+sin4x=2cos(2x+π)cos(2x+π)
(cos2x+sin2x)22cos2xsin2x=cos4x+cos2π
112sin22x=cos4x+1
12(1cos4x2)=cos4x
cos4x=13
sin4x=223
again cos4x=13
12sin22x=13
sin2x=23
Hence, none of the given option is correct.

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