2013.07.

问题描述:

2013.07.
用棣莫弗定理证明:
(1)cos5β=16(cosβ)^5-20(cosβ)^3+5cosβ;
(2)tan5β=[5tanβ-10(tanβ)^3+(tanβ)^5]/[1-10(tanβ)^2+5(tanβ)^4].

cos(5*a)+I*sin(5*a)
= (16*I)*sin(a)*cos(a)^4-(12*I)*sin(a)*cos(a)^2+I*sin(a)+16*cos(a)^5-20*cos(a)^3+5*cos(a)
==>
cos(5*a) = 16*cos(a)^5-20*cos(a)^3+5*cos(a)