sin^4(67.5度) -cos^4(67.5度)

题目

sin^4(67.5度) -cos^4(67.5度)
sin67.5度的4次方 减 cos67.5度的4次方..求值
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答案

先用平方差公式化为(sin^2(67.5度))+cos^2(67.5度))+(
sin^2(67.5度))-cos^2(67.5度))
显然,前面的(sin^2(67.5度))+cos^2(67.5度)=1 后面的=
(sin^2(67.5度))-cos^2(67.5度))用2倍角可化为-cos(2*67.5度)
也就是-cos135=cos45
答案是1+根号2/2