002-11.mws

> expand(cos(2*x));expand(cos(3*x));expand(cos(4*x));expand(cos(5*x));expand(cos(6*x));

2*cos(x)^2-1

4*cos(x)^3-3*cos(x)

8*cos(x)^4-8*cos(x)^2+1

16*cos(x)^5-20*cos(x)^3+5*cos(x)

32*cos(x)^6-48*cos(x)^4+18*cos(x)^2-1

第n 項 等於 2 倍 第n-1 項 乘 cos(x) 減 第 n-2 項

cos(x) cos(x)
cos(2*x) 2*cos(x)^2-1
cos(3*x) 4*cos(x)^3-3*cos(x)
cos(4*x) 8*cos(x)^4-8*cos(x)^2+1
cos(5*x) 16*cos(x)^5-20*cos(x)^3+5*cos(x)
cos(6*x) 32*cos(x)^6-48*cos(x)^4+18*cos(x)^2-1
cos(7*x) 64*cos(x)^7-112*cos(x)^5+56*cos(x)^3-7*cos(x)
64*cos(x)^7-112*cos(x)^5+56*cos(x)^3-7*cos(x)
cos(8*x) 128*cos(x)^8-256*cos(x)^6+160*cos(x)^4-32*cos(x)^2+...
128*cos(x)^8-256*cos(x)^6+160*cos(x)^4-32*cos(x)^2+...
cos(9*x) 256*cos(x)^9-576*cos(x)^7+432*cos(x)^5-120*cos(x)^3...
256*cos(x)^9-576*cos(x)^7+432*cos(x)^5-120*cos(x)^3...
cos(10*x) 512*cos(x)^10-1280*cos(x)^8+1120*cos(x)^6-400*cos(x...
512*cos(x)^10-1280*cos(x)^8+1120*cos(x)^6-400*cos(x...
512*cos(x)^10-1280*cos(x)^8+1120*cos(x)^6-400*cos(x...