What was the difference between the formula that Roger cotes derived and that euler got? I mean to say that Euler got the following formula : $$e^{ix} = \cos x+i \sin x$$
And Cotes got the following : $$ix = \ln(\cos x + i\sin x)$$
We can directly see that it is same as euler's
The problem is that the complex logarithm is multivalued under the current definition. Therefore Cotes' formula is not really true anymore, but it was when he got it.