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Question

If (2sin3xcosx2cos3xsinx)2=2, then x equals to

A
π8
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B
5π8
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C
3π4
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D
3π8
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Solution

The correct options are
A π8
B 5π8
D 3π8
(2sin3xcosx2cos3xsinx)2=2
(2sin(3xx))2=2
sin(AB)=sinAcosBcosAsinB
sin2(2x)=12=(12)2
sin2(2x)=sin2(π4)
2x=nπ±π4, nZ
x=nπ2±π8, nZ

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