cos22.5+sin22.5)(cos^3 22.5-sin^3 22.5)= .算下它的值

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cos22.5+sin22.5)(cos^3 22.5-sin^3 22.5)= .算下它的值
cos22.5+sin22.5)(cos^3 22.5-sin^3 22.5)= .算下它的值

cos22.5+sin22.5)(cos^3 22.5-sin^3 22.5)= .算下它的值
令cos22.5°=x,sin22.5°=y
(x+y)(x³-y³)
=(x+y)(x-y)(x²+xy+y²)
=(x²-y²)(1+2xy/2)
=[cos(2×22.5°)][1+sin(2×22.5°)/2]
=√2/2×(1+√2/4)
(2√2+1)/4
回答完毕.