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.