Identity or Equation?

$\sin\left(x\right)+\cos\left(x\right) = 1$ holds at 0°: 0 + 1. It holds at 90°: 1 + 0. Two checks pass. Is it true at every angle?

Try 60°: $\frac{\sqrt{3}}{2}+\frac{1}{2}$ is about 1.37, not 1. One angle where it fails shows a claim is false. Angles where it works prove nothing. To prove an identity, rewrite one side step by step until it becomes the other side. For example, $\cot\left(x\right)\sin\left(x\right) = \frac{\cos\left(x\right)}{\sin\left(x\right)}\sin\left(x\right)$. The sines cancel, which leaves $\cos\left(x\right)$. It is true wherever both sides have a value.