[Math] Trigonometry, eliminate theta

Question

I've been trying to solve this problem quite for a while but this was all in vain

Eliminate $\theta$ from the equations:
$$x = \sin \theta + \tan \theta, y = \sin \theta – \tan \theta$$

Please help solving this problem.

Answer 1

HINT:

1. Notice that $x+y=2\sin\theta$ and $x-y=2\tan\theta$.
2. Recall that $\tan\theta\equiv\frac{\sin\theta}{\cos\theta}$
3. Recall that $\sin^2\theta + \cos^2\theta \equiv 1$
4. Consider $(x+y)^2$ and $(x-y)^2$ in terms of $\theta$