002-9.mws

> expand(tan(2*x));

2*tan(x)/(1-tan(x)^2)

> expand(tan(3*x));

(3*tan(x)-tan(x)^3)/(1-3*tan(x)^2)

> expand(tan(4*x));

(4*tan(x)-4*tan(x)^3)/(1-6*tan(x)^2+tan(x)^4)

> expand(tan(5*x));

(5*tan(x)-10*tan(x)^3+tan(x)^5)/(1-10*tan(x)^2+5*ta...

下一個函數 等於 [ 前一個函數 + tan(x)] 除以 [1- 前一個函數 乘 tan(x)]

1 tan(x)
2 -2*tan(x)/(-1+tan(x)^2)
3 tan(x)*(-3+tan(x)^2)/(-1+3*tan(x)^2)
4 -4*tan(x)*(-1+tan(x)^2)/(1-6*tan(x)^2+tan(x)^4)
5 tan(x)*(5-10*tan(x)^2+tan(x)^4)/(1-10*tan(x)^2+5*ta...
6 -2*tan(x)*(3-10*tan(x)^2+3*tan(x)^4)/(-1+15*tan(x)^...
-2*tan(x)*(3-10*tan(x)^2+3*tan(x)^4)/(-1+15*tan(x)^...
7 tan(x)*(-7+35*tan(x)^2-21*tan(x)^4+tan(x)^6)/(-1+21...
tan(x)*(-7+35*tan(x)^2-21*tan(x)^4+tan(x)^6)/(-1+21...
tan(x)*(-7+35*tan(x)^2-21*tan(x)^4+tan(x)^6)/(-1+21...
tan(x)*(-7+35*tan(x)^2-21*tan(x)^4+tan(x)^6)/(-1+21...