Prove that sin(x)+(-*2^(1/2))/2=0 is not an identity

 Exercise

$sin\left(x\right)-\frac{\sqrt{2}}{2}=0$

 

Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side

$\sin\left(x\right)=- \frac{-\sqrt{2}}{2}$

 

Multiplying the fraction by $-1$

$\sin\left(x\right)=\frac{\sqrt{2}}{2}$

 

The angles where the function $\sin\left(x\right)$ is $0$ are

$x=45^{\circ}+360^{\circ}n,\:x=135^{\circ}+360^{\circ}n$

 

There is no identity or mathematical rule that allows us to proceed trying to match both sides of the equality, so we conclude that it is not true

The equation is not an identity

The equation is not an identity

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