Solve Trig Equation tan 2x = 8cos^2 x - cot x for x 0 ≤ x ≤ pi/2

[John H]

Homework Statement

tan 2x = 8cos^2 x - cot x. Solve where x 0 ≤ x ≤ pi/2

Homework Equations

The basic trig identities

The Attempt at a Solution

I tried many different things which all eventually led to no solution. Firstly I tried solving the problem as I would a rational equation. So all terms were collected on one side of equation, and tangent and cotangent were made into sins and cosines, and the entire set of term were then written as one rational expression. Yet no solutions arouse from this method. Help appreciated. If necessary I will scan a copy of my work thus far.

 

[Integral]

Show us what you have done.

 

[hunt_mat]

Turn everything into sin and cos and multiply by sin x/cos x, you should be able to then cancel a cos x. Re-arrange to obtain a simple equation which you can then solve.

Mat

 

[HallsofIvy]

It will help to know that
$$tan(2x)= \frac{2tan(x)}{1- tan^2(x)}$$

 

[hunt_mat]

Not really, it won't. He needs to turn everything into either sin x or cos x. he can just use tan(2x)=sin(2x)/cos(2x)