$\displaystyle tan \frac{3\pi}{8}$
Use $\displaystyle tan 2\theta$ to find the exact value
Im stuck because I dont know which half-angle formula do I use?
I have given the half angle formula.
If 2θ = 3π/4, half of that angle is θ = 3π/8 which is the required angle.
I have observed that you are not following our instructions. Every time you expect the complete solution. It is not good for any student who wants to study the subject.
In my post, you have to find the value of tan(3π/4), simplify the expression, solve the quadratic equation to get tanθ, i.e. tan(3π/8).
Can you try now?
$\displaystyle \tan\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1-\cos{\theta}}{1+\cos{\theta}}}$
if $\displaystyle \frac{\theta}{2} = \frac{3\pi}{8}$ , then $\displaystyle \theta = \frac{3\pi}{4}$
also note that $\displaystyle \frac{3\pi}{8}$ is a quad I angle, so $\displaystyle \tan\left(\frac{3\pi}{8}\right) > 0
$
plug and chug using the given half-angle formula.