cot7a
= 1-21tan^2a+35tab^4a-7tan^6a/(7tana-35tan^3a+21tan^5a-tan^7a)
for cot7a=0 , cos7a = 2n兀+/- 兀/2 where n is any integer
=> 1-21tan^2a+35tab^4a-7tan^6a = 0
show that
tan^2(兀/14) , tan^2(3兀/14) and tan^2(5兀/14) are the roots of
7x^3-35x^2+21x-1=0
更新1:
why?? cot7a = 0 => cot na/7 where n = 1,....,6
更新2:
sub a = pi/7, 2pi/7, ... , 6pi/7 into cot7a=0 It is undefined!
