Can I prove a proportionality equation by cross multiplying? If yes, then can I prove a trig identity that is a proportionality equation using cross multiplication? My teacher said we cannot "work across the equals sign"

Question

skullpatrol · Answer

You are not "proving" a proportion by cross multiplying. 

Instead what you are doing is solving an equation to get a solution set. 

With trig identities you are proving that one side is the same as the other, so you can't cross multiply.

anthonyym · Answer

So if I have
$$\frac{ 1 }{ 2 }=\frac{ 4 }{ 8 }$$
I cannot prove this proportion by writing
1*8 = 4*2
8 = 8

skullpatrol · Answer

Yes, that is one way to show that they are equal. But you are dealing with only numerals and not variables, right?

anthonyym · Answer

Yes

skullpatrol · Answer

With variables you have to be careful that no denominator equals 0.

anthonyym · Answer

But you wouldn't write the proportion to prove if the denominator was already 0.
I wouldn't write 1/0 = 4/8 and say prove the identity if it's already divided by 0.