# Question #97e1b

Jan 15, 2018

$x = \pi \cdot n$ where $n \in \mathbb{Z}$.

#### Explanation:

The Pythagorean Identity says: ${\cos}^{2} \left(x\right) + {\sin}^{2} \left(x\right) = 1$ which means we can rewrite the original:

$2 {\sin}^{2} \left(x\right) = 1 - 1 \rightarrow 2 {\sin}^{2} \left(x\right) = 0 \rightarrow \sin \left(x\right) = 0$

If $\sin \left(x\right) = 0$ we know $x = 0 + 2 \pi \cdot n$ where $n \in \mathbb{Z}$ or $x = \pi + 2 \pi \cdot n$ where $n \in \mathbb{Z}$.

We could also simplify this to $x = \pi \cdot n$ where $n \in \mathbb{Z}$.