Q:

Difference between the formula of Roger Cotes and Euler

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

A:

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. 

