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Question

The value of cos4(π8)+cos4(3π8)+cos4(5π8)+cos4(7π8) is equal to

A
12
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B
34
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C
32
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D
1
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Solution

The correct option is C 32

cos4π8+cos43π8+cos45π8+cos47π8=cos4π8+cos43π8+cos4(π3π8)+cos4(ππ8)=2(cos4π8+cos43π8)=2(cos4π8+cos4(π2π8))=2(cos4π8+sin4π8)=2(12sin2π8cos2π8)=2(112sin2π4)=2(112.12)=32


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