已知sina是方程6x=1-根号x的根

6x=1-√x
√x=1-6x
x=36x^2-12x+1
36x^2-13x+1=0
(9x-1)(4x-1)=0
x=1/4,x=1/9
经检验x=1/4是增根
所以sina=1/9
cosa=±√[1-(sina)^2]=±4√5/9
tana=±√5/20

cos(a-5π)tan(2π-a)/cos(3π/2-a)cot(π-a)
=cos(a-5π+6π)tan(2π-a-2π)/cos(3π/2-a-2π)cot(π-a-π)
=cos(π+a)tan(-a)/cos(-a-π/2)cot(-a)
=cosatana/sinacota
=sina/cosa
=tana
=±√5/20

x=(1-6x)^2
36x^2-13x+1=0
x=1/9

cos(a-5兀)*tan(2兀-a)/cos(3兀/2-a)*cot(兀-a)
=cos(a)*tan(a)/sin(a)*cot(a)
=sin(a)/cos(a)
=tan(a)
=x/sqrt(1-x^2)
=sqrt(5)/20