Final Answer
The equation is not an identity
Step-by-step Solution
Problem to solve:
$\sin\left(x\right)- \frac{\sqrt{2}}{2}=0$
Specify the solving method
1
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
Since we're dealing with trig functions, we can try with different angles as input, such as: $0^{\circ}, 30^{\circ}, 60^{\circ}, 90^{\circ}, 180^{\circ}...$
2
If we try with the following value
$x=0$
Replace the variable $x$ with the value $0$
$\sin\left(0\right)-\frac{\sqrt{2}}{2}$
Divide $-\sqrt{2}$ by $2$
$\sin\left(0\right)-\frac{\sqrt{2}}{2}$
The sine of $0$ equals $0$
$-\frac{\sqrt{2}}{2}$
3
After substituting the value and simplify on the left side, we get
$-\frac{\sqrt{2}}{2}$
Replace the variable $x$ with the value $0$
0
4
After substituting the value and simplify on the right side, we get
0
5
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
The equation is not an identity
Final Answer
The equation is not an identity