cosx=[e^(ix)+e^(-ix)]/2

sinx=[e^(ix)-e^(-ix)]/(2i)

Can also be expanded into a series of forms:

sinx=x-x^3/3！ +x^5/5！ - ...

cosx= 1-x^2/2！ +x^4/4！ +

Extended data (1) When R= 2, from the description of 1, these two regions can be imagined as two hemispheres with the equator as the boundary, and there are two "vertices" on the equator that divide the equator into two "boundaries", namely, R= 2, V= 2, and E = 2；; So R+ V- E= 2, euler theorem is established.

(2) Let R= m(m≥ 2) and euler theorem is established. It is proved that euler theorem also holds when R= m+ 1.

Baidu Encyclopedia-Euler Formula