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Question

The expression 3[sin4(3π2α)+sin4(3π+α)]2[sin6(π2+α)+sin6(5π+α)] is equal to


A

0

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B

1

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C

3

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D

sin4α+cos6α

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Solution

The correct option is B

1


3[sin4(3π2α)+sin4(3π+α)]2[sin6(π2+α)+sin6(5π+α)]

=3[cos4α+sin4α]2[cos6α+sin6α]

=3cos4α+3sin4α2cos4α(1sin2α)2sin4α(1cos4α)

=sin4α+cos4α+2cos4αsin2α+2sin4αcos2α

=(sin2α+cos2α)22sin2αcos2α+2cos2αsin2α(cos2α+sin2α)

=12sin2αcos2α+2cos2αsin2α

=1


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