sin²(x) can be written in terms of an infinite sum over cos²(x) [and vice versa]pic.twitter.com/avj4yy6SPe
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Except for almost all complex values.
well my original tweet was concerning real numbers.. but let's see the endpoints in the complex plane are the z such that |cos^2(z)|=1 and so would be a condition as a function of e^{ix} e^{y} that i don't feel like working out
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The modulus of cos(x+iy) is bigger than abs(e^y-e^(-y))/2. So, the series does not converge outside band around the real axis
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In fact, the series converges in the gray area, and diverges in the white one.pic.twitter.com/oB26d1XxY0
End of conversation
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