What is $cos(ln(x))$ ?

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Answer 1 · 2016-12-20T00:11:55

$cos(ln(x)) = (x^i+x^(-i))/2$

Given that:

$e^(i theta) = cos theta + i sin theta$

$cos (-theta) = cos(theta)$

$sin (-theta) = -sin(theta)$

we can deduce that:

$cos(theta) = (e^(itheta) + e^(-itheta))/2$

So:

$cos(ln(x)) = (e^(ilnx)+e^(-ilnx))/2$

$color(white)(cos(ln(x))) = ((e^(lnx))^i+(e^(lnx))^(-i))/2$

$color(white)(cos(ln(x))) = (x^i+x^(-i))/2$

What is cos(ln(x))cos(ln(x))?