Why did my trigonometry instructor advise me to use 'or' instead of $\implies$?

Question

I was solving a trigonometric equation today and was using the $\implies$ symbol after every step. Seeing this, my instructor advised me not to use this symbol but use $or,$ after every step. He cited that $\implies$ symbol is used majorly in abstract algebra, and although there is a very fine difference between the two and the two may be interchanged, he advised not use $\implies$.

But it's not clear to me why. Please explain it to me.

For example

I wrote $\dfrac{\sin A \cos B}{\cos A \sin B}=m\implies\dfrac{\sin A \cos B -\cos A \sin B}{\sin A \cos B + \cos A \sin B}=\dfrac{m-1}{m+1}$.

He told me to replace the $\implies$ by 'or'.

Answer 1

This is wrong; are you sure you understood your instructor correctly?

The symbol $\Rightarrow$ is not used any more in abstract algebra than anywhere else, and it is not a reason to avoid using $A \Rightarrow B$. Additionally, "or" doesn't mean the same thing as "implies": indeed, "true or false" is true, while "true implies false" is false.

Answer 2

There is a convention (in Indian high school math classes but maybe also elsewhere) to use "or" as a connective between equations or statements, with more or less the same semantics as "that is" or "i.e.". If you're only using the implication in the forward direction, it is clearer and easier on the reader to use $\implies$. In case your operation is not obviously reversible I would not use "or"; the semantics of "or" should always be symmetric. For example, "$\sin x = \sqrt{3} \cos x \implies \sin^2 x = 3 \cos^2 x$" is correct while "$\sin x = \sqrt{3} \cos x$, or, $\sin^2 x = 3 \cos^2 x$" at best requires more justification.