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Question

Find cos4(π/8)+cos4(3π/8)+cos4(5π/8)+cos4(7π/8)3/2

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Solution

cos4(π/8)+cos4(3π/8)+cos4(π3π8)+cos4(ππ8)3/2
=cos4(π/8)+cos4(3π/8)+cos4(π/8)+cos4(3π/8)3/2
=2cos4(π/8)+2cos4(3π/8)3/2
=2[cos4(π/8)+cos4(3π/8)]3/2
π8=(2212)
3π8=(6612)
puting values
=2[(0.9238)4+(0.38268)4]3/2
=2[0.72855+0.02144]1.5
=1.51.5
=0


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