1)How would you verify this numerically?

there is no given value of x so Im confused just use a calculator?

(pi/2+x)=sin(pi/2-x)

2)even when you get a given value of x I get confused like

cos(pi-x)=-cosx

when x=2.9

3)also if you are given a list of possible identities and are asked to say which ones are and which ones arent how do you do that? Just sketch it, I mean it worked for me but if you have a easier way Id love any input.

example

tan-x=tanx

tan-x=-tanx

sin(pi/2+x)=cosx

sin(pi/2-x)=cosx

thanks.