Why to simplify $\sin x - 1 =\cos x$ you have to multiply both side by $(\frac{\sqrt 2}{2}) $? Why do you have to multiply both side of $$\sin x - 1 = \cos x$$
by:
$$(\frac{\sqrt 2}{2}) $$ to simplify it?
I am doing Shaum's pre-calculus and the final answer to this question is: π but I have no clue where the idea of multiplying by $(\frac{\sqrt 2}{2})$ came from. Like what is the taught process behind it?

Another solution you can consider is $$\sin x -\cos x = 1$$ then square both sides to get $$\sin^2x - 2\sin x \cos x + \cos^2x = 1$$ so $$-2\sin x \cos x  = 0$$
This is equivalent to $\sin(2x) = 0$, so $x$ is any $\frac{n\pi}{4}$ , $n \in \mathbb{Z}$ 
However, a danger with this approach is that you may introduce extra solutions; as when $$\sin^2x - 2\sin x \cos x + \cos^2x = 1$$ this also introduces $$\sin x -\cos x = -1$$ as possible roots.
