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...................

Question

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
...................

Answer 1

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