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Question

The value of
cos2(π16)+cos2(3π16)+cos2(5π16)+cos2(7π16) is

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Solution

From given expression we can see that
π16,7π16 and 3π16,5π16 are complementry angles

cos2(π16)+cos2(3π16)+cos2(5π16)+cos2(7π16)

=[cos2(π16)+cos2(7π16)]+[cos2(3π16)+cos2(5π16)]

=[cos2(π16)+cos2(π2π16)]+[cos2(3π16)+cos2(π23π16)]

=[cos2(π16)+sin2(π16)]+[cos2(3π16)+sin2(3π16)]
=1+1=2

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