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Prove that $\sin\left(x\right)- \frac{\sqrt{2}}{2}=0$ is not an identity

Step-by-step Solution

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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

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Verify if true (using algebra)

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