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Question: How do i solve equations of trig with high degree

Question:How do i solve equations of trig with high degree

beidouxing 10 Maple
solve trigonometric
January 18 2015
1


eqn1 := (3*y/(y^2+1)^(5/2)+(3*(x+y))/(1+(x+y)^2)^(5/2)+(3*(y+z))/(1+(y+z)^2)^(5/2)+(3*(x+y+z))/(1+(x+y+z)^2)^(5/2))*(-2*x^2/(x^2+1)^2+1/(x^2+1)-2*x*(x+y)/(1+(x+y)^2)^2+1/(1+(x+y)^2)-2*x*(x+z)/(1+(x+z)^2)^2+1/(1+(x+z)^2)-2*x*(x+y+z)/(1+(x+y+z)^2)^2+1/(1+(x+y+z)^2))+(-3*x/(x^2+1)^(5/2)-(3*(x+y))/(1+(x+y)^2)^(5/2)-(3*(x+z))/(1+(x+z)^2)^(5/2)-(3*(x+y+z))/(1+(x+y+z)^2)^(5/2))*(-2*y^2/(y^2+1)^2+1/(y^2+1)-2*y*(x+y)/(1+(x+y)^2)^2+1/(1+(x+y)^2)-2*y*(y+z)/(1+(y+z)^2)^2+1/(1+(y+z)^2)-2*y*(x+y+z)/(1+(x+y+z)^2)^2+1/(1+(x+y+z)^2)):

eqn2 := x/(x^2+1)+x/(1+(x+y)^2)+x/(1+(x+z)^2)+x/(1+(x+y+z)^2)-y/(y^2+1)-y/(1+(x+y)^2)-y/(1+(y+z)^2)-y/(1+(x+y+z)^2):

eqn3 := subs({x = (tan(alpha)-tan(beta)+tan(gamma))*(1/2), y = (tan(alpha)+tan(beta)-tan(gamma))*(1/2), z = (-tan(alpha)+tan(beta)+tan(gamma))*(1/2)}, eqn1):

eqn4 := subs({x = (tan(alpha)-tan(beta)+tan(gamma))*(1/2), y = (tan(alpha)+tan(beta)-tan(gamma))*(1/2), z = (-tan(alpha)+tan(beta)+tan(gamma))*(1/2)}, eqn2):

My question is how to solve eqn3 and eqn4 of tan(alpha)&&tan(beta).

I want to solve the equations eqn3 and eqn4 to solve the  tan(alpha)  and tan(beta),  give me a help .thanks a lot 

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