Studying Mathematics Thread

[GrandizerII]

Some trigonometry fun:

tanx = sinx/cosx

cotx = cosx/sinx

Is tanx = 1/cotx? And is cotx = 1/tanx?

It seems like the answer to both is "no", but I could be mistaken. Correct me if so.

Here's my [probably mathematically naive] reasoning:

If x = 0, then tanx = sinx/cosx = 0, while 1/cotx = 1/(cosx/sinx) is undefined (since sin(0) = 0). Therefore, tanx != 1/cotx.

If x = pi/2, then cotx = cosx/sinx = 0, while 1/tanx = 1/(sinx/cosx) is undefined (since cos(pi/2) = 0). Therefore, cotx != 1/tanx.