Deduce THIS!
Hey everyone,
Let's say that we have f(x) = ln(1 + sinx). We then determine this function's Maclaurin series.
If I wanted to determine the Maclaurin series for g(x) = ln(1 - sinx), I am told that it can be deduced from f(x). (I don't have to derivate for the second series; I can instead add something to every term of the first series.)
But how? What kind of additions can be made to ln(1 + sinx) to reach ln(1 - sinx) without adding something whose Maclaurin series is not readily available to me?
I'm quite sure I have to take advantage of logarithmic identities and/or angle formulas, but I don't know where to start.
Thanks.
Let's say that we have f(x) = ln(1 + sinx). We then determine this function's Maclaurin series.
If I wanted to determine the Maclaurin series for g(x) = ln(1 - sinx), I am told that it can be deduced from f(x). (I don't have to derivate for the second series; I can instead add something to every term of the first series.)
But how? What kind of additions can be made to ln(1 + sinx) to reach ln(1 - sinx) without adding something whose Maclaurin series is not readily available to me?
I'm quite sure I have to take advantage of logarithmic identities and/or angle formulas, but I don't know where to start.
Thanks.