How can I solve these trigonometric equations?

[kristo]

Homework Statement

The original problem is this: ab^2*cos(2x)*(cos(x))^2 + ba^2*sin(2x)*(sin(x))^2 = 0
And some of the more "logical" forms I've got to are these:2[tan(x)]^3-2tan(x) = -b/a
tan(2x)*(tan(x))^2=-b/a
But I can't solve these equations so I'd like to ask for some help here.

 

[tiny-tim]

Hi kristo!

(try using the X² tag just above the Reply box )

tan(2x)*(tan(x))^2=-b/a

That's the one!

Now just write tan(2x) in terms of tanx, and solve. ​

(eugh … it's a cubic )

 

[alijav]

try to assign a variable like u to tanx
then establish a relation between tanx and tan2x
and then write both equations in terms of u and equate both to each other
and then solve the resultant equation for u