cis(x) Variation

[Srd2000]

Hello, is there anyone way to simplify icos(x)+sin(x)  I've found that d/dz (cis(z) = icis(z) = icos(z)-sin(z), but what if it were +sin(z) instead?

Thank you

[RuiAce]

Hello, is there anyone way to simplify icos(x)+sin(x)  I've found that d/dz (cis(z) = icis(z) = icos(z)-sin(z), but what if it were +sin(z) instead?

Thank you

\begin{align*} i\cos x + \sin x &= i\cos (-x) - \sin (-x)\\ &= i \left( \cos (-x) + i\sin (-x) \right) \end{align*}
Usually, if you can't keep \(x\) there, you need to replace it with \(-x\).