I've always been taught to write, for example, $$\sin^2(\theta)+\cos^2\theta \color{red}{\equiv} 1,$$ rather than $$\sin^2(\theta)+\cos^2\theta \color{red}{=} 1,$$ and $$x(x+2)\color{red}{\equiv} x^2+2x$$ rather than $$x(x+2)\color{red}{=}x^2+2x, $$as $\equiv$ denotes an identity, so the equation is true for all values of the variable(s), whereas $=$ is an equation that only holds for some specific values of the variable.
I've happily taken this on board, but I've seen so few people write it.
In this context only (i.e. with regards to identities), are $=$ and $\equiv$ interchangeable, or have I been lied to/deceived?
Are both correct in this situation?
Thanks
$\endgroup$ 61 Answer
$\begingroup$The $\equiv$ symbol indeed is used when the values are identical, independent of the variable. For example, if $f(x) = 0 \quad \forall x$, then we write $f \equiv 0$. Write $x(x+2) \equiv x²+2x$ is correct also, because it is true for all x. However, people really don't give it so much importance, it serves just as a reminder.
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