Question

Proving $\sec^3\frac{2\pi}{7}+\sec^3\frac{4\pi}{7}+\sec^3\frac{6\pi}{7}=-88$ and $\sec^2\frac{2\pi}{7}+\sec^2\frac{4\pi}{7}+\sec^2\frac{6\pi}{7}=24$

score 115 · Answer 1 · 2026-04-15 18:15:11

115

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Proving $\sec^3\frac{2\pi}{7}+\sec^3\frac{4\pi}{7}+\sec^3\frac{6\pi}{7}=-88$ and $\sec^2\frac{2\pi}{7}+\sec^2\frac{4\pi}{7}+\sec^2\frac{6\pi}{7}=24$

Published on 15 Apr 2026 - 18:15

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List Question

Proving $\sec^3\frac{2\pi}{7}+\sec^3\frac{4\pi}{7}+\sec^3\frac{6\pi}{7}=-88$ and $\sec^2\frac{2\pi}{7}+\sec^2\frac{4\pi}{7}+\sec^2\frac{6\pi}{7}=24$

Winning strategy of Peter such that quadratic equations has Rational roots

Do all odd functions have symmetric zeros?

Proving the existence and number of real roots for $x^3 - 3x + 2$

Find how many roots of $z^5+2z^2+7z+1=0$ lie inside $|z|=2$? How many are real?

Solving an equation involving the real and complex roots of the function

Does Rouche's Theorem apply INSIDE and ON the contour?

Complex solutions of $z^n = w$, where $n \in \mathbb N^*$ and $w \in \mathbb C.$

Newton and Secant method using MATLAB

minimal polynomial of $1+\alpha^2$ where $\alpha$ is a root of $x^3-x-1$

If $r$ is the root of an equation, $1/r$ will be the root of what equation?

How to create a polynomial with a variable root

zeta function, a nontrivial zero that is not on critical line

Sum of roots of any equation

Show that the roots of $x^2 − 2α x +β = 0$ are $x = α \pm \sqrt {α^2 −β}$

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