x（角）余弦的八次方减去x的正弦的八次方再加上四分之一倍的这个2x的正弦成上4x的正弦 对这个式子化简
问题描述：
x（角）余弦的八次方减去x的正弦的八次方再加上四分之一倍的这个2x的正弦成上4x的正弦 对这个式子化简
答
cos^8(x) - sin^8(x) + (1/4)sin2xsin4x
= [cos^4(x) + sin^4(x)]*[cos^4(x) - sin^4(x)] + (1/4)*sin2x * 2*sin2x*cos2x
=[cos^4(x) + 2*cos^2(x)*sin^2(x) + sin^4(x) - 2*cos^2(x)*sin^2(x)] * [cos^2(x) + sin^2(x)]*[cos^2(x) - sin^2(x)] + (1/2)*(sin2x)^2 * cos2x
= [1 - 2*cos^2(x) * sin^2(x)]*cos2x + (1/2)*(sin2x)^2 * cos2x
= [1 - (1/2)* (sin2x)^2] * cos2x + (1/2)* (sin2x)^2 * cos2x
= cos2x
答
(cosx)^8-(sinx)^8+1/4*sin2x*sin4x=[(cosx)^4+(sinx)^4][(cosx)^4-(sinx)^4]+1/4*sin2x*2sin2xcos2x={[(cosx)^2+(sinx)^2]^2-2(cosx)^2(sinx)^2}[(cosx)^2+(sinx)^2][(cosx)^2-(sinx)^2]+1/2*(sin2x)^2cos2x=[1-2(c...