Solve Trig Question: tan(2θ) = cot(φ)

[jesuslovesu]

[SOLVED] Trig Question

Homework Statement

Let's say I have $$tan(2\theta) = cot(\phi)$$ I'm not quite sure how to simplify it (I want to solve for theta) I could say $$tan(2\theta) = 1 / tan(\phi)$$
$$2\theta = atan( 1 / tan(\phi) )$$ but then I'm not sure what to do after that.
Do I take the atan of 1 and $$tan(\phi)$$?

I know another method to find it is to say $$cot(\phi) = \pi/2 - tan(\phi)$$ but I don't understand that either because $$2\theta = atan( \pi/2 - tan\phi ) != \pi/2 -\phi$$ (not exactly at least)
The answer as far as I know is supposed to be $$2\theta = \pi/2 -\phi$$

 

[rock.freak667]

Remember that that the tangent of angle is the cotangent of its complement and go from that definition.

OR you could say that


$$tan(2\theta) = cot(\phi) \Rightarrow \frac{2tan\theta}{1-tan^2\theta}=\frac{1}{tan\phi}$$

and solve from there.

Two ways really, one is easier than the other though.