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Question

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

A
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B
1
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C
1
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D
3
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Solution

The correct option is B 1
3[sin4(3π2α)+sin4(3π+α)]2[sin6(π3+α)+sin6(5πα)]
=3[cos4α+sin4α]2[cos6α+sin6α]
=3[(sin2α+cos2α)22sin2αcos2α]2[(sin2α+cos2α)33sin2αcos2α(sin2α+cos2α)]
=36sin2αcos2α2+6sin2αcos2α=1

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