Theory The difference quotient: f(a+h)−f(a)h\frac{f(a+h)-f(a)}{h}hf(a+h)−f(a) Identities used: sinu−sinv=2cos(u+v2)sin(u−v2)\sin u-\sin v=2\cos\left(\frac{u+v}{2}\right)\sin\left(\frac{u-v}{2}\right)sinu−sinv=2cos(2u+v)sin(2u−v) tanα−tanβ=sin(α−β)cosαcosβ\tan\alpha-\tan\beta=\frac{\sin(\alpha-\beta)}{\cos\alpha\cos\beta}tanα−tanβ=cosαcosβsin(α−β)