** Final Answer

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** Step-by-step Solution **

Problem to solve:

** Specify the solving method

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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

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If we try with the following value

Replace the variable $x$ with the value $0$

Divide $-\sqrt{2}$ by $2$

The sine of $0$ equals $0$

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After substituting the value and simplify on the left side, we get

Replace the variable $x$ with the value $0$

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After substituting the value and simplify on the right side, we get

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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

** Final Answer

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