Verifying trig identities.... what about when tan is undefined?

[srfriggen]

TL;DR

Do trig identities have restricted domains?

Hello,

If I wanted to verify tan(x)cos(x) = sin(x), what about when x is pi/2? LHS has a restricted domain so it can't equal sin(x). Does this equation only work with a restricted domain? Nothing in my textbook discusses that.

Thank you

 

[mfb]

You can verify that tan(x)cos(x) = sin(x) for all x where the left side is defined. That's as good as it gets.

 

[Office_Shredder]

Here's a similar question. Is x/x=1? There's nothing special about trig identities potentially having holes in the domain.

One thing that is true is that as x approaches pi/2, tan(x)cos(x) approaches sin(pi/2), so if you're willing to extend the function continuously, then you get equality everywhere