What are five trigonometric identities?

All others can be derived from these and a little calculus:

sin2x+cos2x=1

sec2x-tan2x=1

sin(a+b)=sin(a)cos(b)+sin(b)sin(a)

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

eix=cos(x)+i*sin(x)