The conversation between human and AI assistant.
How can we learn all the trigonometric formulae with Euler's formula?
Wow, that's really helpful. Can we do the same thing to derive the formula for tangent?
Yes, we can. We start by dividing the formula for sine by the formula for cosine, which gives us sin(x)/cos(x) = (e^(ix) - e^(-ix))/(i*(e^(ix) + e^(-ix))). Simplifying that expression using the rules of algebra gives us the formula for tangent: tan(x) = sin(x)/cos(x) = (e^(ix) - e^(-ix))/(i*(e^(ix) + e^(-ix))).