Learn How to Express cos(2x) as sin(x) Using Complex Exponential Series

[n0_3sc]

This is an easy question but can some else show/tell me how to do it:
"use the complex exponential series to express cos(2x) in terms of sin(x)"
I also don't quite understand the 'complex exponential series'.

 

[n0_3sc]

I mean can someone* show/tell me...

 

[cookiemonster]

$$e^{i\theta} = \cos{\theta} + i\sin{\theta}$$

$$e^{i\theta} + e^{-i\theta} = 2\cos{\theta}$$

$$e^{i\theta} - e^{-i\theta} = 2i\sin{\theta}$$

cookiemonster

 

[fourier jr]

complex exponential series is just the taylor series for exp except with a complex variable instead of a real one