计算cos^4(π/8)+sin^4(π/8)=____ 怎么做的?

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计算cos^4(π/8)+sin^4(π/8)=____怎么做的?计算cos^4(π/8)+sin^4(π/8)=____怎么做的?计算cos^4(π/8)+sin^4(π/8)=____怎么做的?c

计算cos^4(π/8)+sin^4(π/8)=____ 怎么做的?
计算cos^4(π/8)+sin^4(π/8)=____ 怎么做的?

计算cos^4(π/8)+sin^4(π/8)=____ 怎么做的?
cos^4(π/8)+sin^4(π/8)
=(cos^2(π/8)+sin^2(π/8))^2-2cos^2(π/8)sin^2(π/8)
=1-0.5sin^2(π/4)
=3/4

cos^4(π/8)+sin^4(π/8)=(cos^2(π/8)+sin^2(π/8))^2-2cos^2(π/8)×sin^2(π/8))=1-2×(0.5sin(π/4))^2=1-2×(1/8)=3/4=0.75