Why are extraneous solutions created here?

Question

So I understand this trigonmetric identify. I'm just wondering why the extraneous solutions are created. What's the intuition?

I see why we need to square both sides... we can then make use of $sin^2\theta + cos^2\theta = 1$.

But why are the extraneous solutions created?

Answer 1

That is simply because $$A^2=B^2\iff A=B\quad\text{ OR }\quad \color{red}{A=-B}.$$