I'm unable to solve this question:
$\cos(\theta)=\dfrac{\cos(\alpha)+\cos(\beta)}{1+\cos(\alpha) \cos(\beta)}$
Prove: $\tan^2\left(\frac\theta2\right)= \tan^2\left(\frac\alpha2\right)\tan^2\left(\frac\beta2\right)$
I have tried the following:
- Using the indentity: $\cos(\theta)=\dfrac{1-\tan^2\left(\frac\theta2\right)}{1+\tan^2\left(\frac\theta2\right)}$
- Diving by $\cos (\alpha) \cos (\beta)$
- Creating a triangle, to find $\tan(\theta)= \sin \alpha \sin \beta$
Every time I got a huge complex equation with roots. Any help would be appreciated.