Why can they just trigonometric functions by x? Won't that mess up/change the original equation?

[bbm25]

How do they just divide by x like that? I understand if they rationalize by multiplying by x/x but i don't get how they do something like this. Doesn't it change the original equation?

 

[Dr.Peterson]

I think you meant to say, "Why can they just divide trigonometric functions by x? Won't that mess up/change the original expression?"

They are doing what we always do with fractions: multiply or divide both numerator and denominator by the same thing, which doesn't change its value. Dividing both by x is no different from multiplying both by x (as long as x is not zero -- and it isn't while you take the limit). To put it differently, they are multiplying by (1/x)/(1/x), which is 1.

 

[bbm25]

Thank you! I understand exactly what it means now