Representation theory of $U(2)$

How do we prove $\cos(\pi/5) - \cos(2\pi/5) = 0.5$ ?.

Complex Analysis Solution to the Basel Problem ($\sum_{k=1}^\infty \frac{1}{k^2}$)

Partial fraction with a constant as numerator

Getting the sequence $\{1, 0, -1, 0, 1, 0, -1, 0, \ldots\}$ without trig?

Proving that: $\lim\limits_{n\to\infty} \left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)^n =\sqrt{ab}$

Hard planar graph problem

Residue integral: $\int_{- \infty}^{+ \infty} \frac{e^{ax}}{1+e^x} dx$ with $0 \lt a \lt 1$.

Hamiltonian Path Detection

$F/K$ finite extension, then $\exists !$ intermediate field $K \subset L \subset F$ such that $L/K$ separable and $F/L$ purely inseparable

Encyclopedia of Groups

Prove $\gcd(nn!, n!+1)=1$

Improper integral of $\frac{x}{e^x-1}$

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