To prove that an equation is not an identity, we only need to find one input at which both sides of the equation result in different values
If we try with the following value
After substituting the value and simplify on the left side, we get
After substituting the value and simplify on the right side, we get
Since the values of $\sin\left(x\right)+\frac{-\sqrt{2}}{2}$ and $0$ are unequal for $x=0$, we conclude that the equation is not an identity
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