I'm asked to solve $\tan{x} = \tan{3x}$ Here's my attempt: $$\tan{x} = \tan{3x}$$ $$\tan{x} = \tan{(x + 2x)}$$ $$\tan{x} = \frac{\tan{x} + \tan{2x}}{1-\tan{x}\tan{2x}}$$ Recall the identity: $$\tan{2x} = \frac{2\tan{x}}{1-\tan^2{x}}$$ So then we have: $$\tan{x} = \frac{\tan{x} + \frac{2\tan{...

I'm looking for methods on how to solve; $$a_1 \sin (x+y) + a_2 \sin (x-y)=0$$ where 1) $a_1, a_2$ are constants 2) $a_1, a_2$ are functions of $x$ and $y$