I would like to know the clarification of the following.
If the follwoing one is correct, we can find cosix and sin ix series very quickly.
We know that, Cosx + i sinx = e^ix
If we replace x by ix on both sides, we get; cos ix + i sin i x = 1/e^x
we know that e^-x series. In this by taking real part and imaginary part and then equating to LHS, can we get cos ix and sinix series. If it is wrong? why it is wrong...justify. Thanks in advance