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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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###  Videos

The equation is not an identity

##  Step-by-step Solution 

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: $0^{\circ}, 30^{\circ}, 60^{\circ}, 90^{\circ}, 180^{\circ}...$
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If we try with the following value

$x=0$
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After substituting the value and simplify on the left side, we get

$-\frac{\sqrt{2}}{2}$
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After substituting the value and simplify on the right side, we get

0
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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

The equation is not an identity

The equation is not an identity

##  Explore different ways to solve this problem

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Verify if true (using algebra)

### Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.