Final Answer
Step-by-step Solution
Problem to solve:
Specify the solving method
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
Replace the variable $x$ with the value $0$
Divide $-\sqrt{2}$ by $2$
The sine of $0$ equals $0$
After substituting the value and simplify on the left side, we get
Replace the variable $x$ with the value $0$
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