Newbetuts

Show $\sin(a+b)+\sin(a+c)+\sin(b+c)-\sin a-\sin b-\sin c-\sin(a+b+c)=8\sin\frac{a}{2}\sin\frac{b}{2} \sin \frac{c}{2} \cos \frac{a+b+c}{2}$

Let $\omega=e^{i2\pi/2015}$, evaluate $\sum\limits_{k=1}^{2014}\frac{1}{1+\omega^k+\omega^{2k}}$

Solving $45x-3795x^3 +95634x^5 - \cdots + 945x^{41}-45x^{43}+x^{45} = N$?

Limit of the sequence $a_{n+1}=\frac{1}{2} (a_n+\sqrt{\frac{a_n^2+b_n^2}{2}})$ - can't recognize the pattern

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

Interesting infinite nested square roots of 2 for $2\cos1°$ and $2\sin1°$

Find the Maximum Trigonometric polynomial coefficient $A_{k}$

In deriving the catenary equation, how does integrating $\frac{dy'}{\sqrt{1+(y')^2}}=\frac1a dx$ yield $\sinh^{-1}(y')=\frac{x}{a}$?

How to find finite trigonometric products [closed]

When does $a \cdot\sin(x) = \sin(a \cdot x)$?

Prove trig identity: $\tan(x) + \cot(x) = \sec(x) \csc(x)$ wherever defined

$\sum_{i=1}^{89} \sin^{2n} (\frac{\pi}{180}i)$ is a dyadic rational

Evaluate $\int\frac {\csc^2{x}-2005}{\cos^{2005}{x}} dx $

solve $\frac{\sqrt{5}(\cos \theta - \sin \theta)}{3\sqrt{2}}=\tan \theta$

Are there polynomials in $\mathbb{R}[x]$, other than $P(x)=x^2$, such that $P(\sin x)+P(\cos x)=1$ for all real $x$?

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Prove that $a_1 \cos(b_1 x) + \dots + a_n \cos(b_n x)$ has zero

Finding the position where a picture was taken

Conjecture about a point inside an equilateral triangle divided by integer angles

What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$?

Show $\sin(a+b)+\sin(a+c)+\sin(b+c)-\sin a-\sin b-\sin c-\sin(a+b+c)=8\sin\frac{a}{2}\sin\frac{b}{2} \sin \frac{c}{2} \cos \frac{a+b+c}{2}$

Let $\omega=e^{i2\pi/2015}$, evaluate $\sum\limits_{k=1}^{2014}\frac{1}{1+\omega^k+\omega^{2k}}$

Solving $45x-3795x^3 +95634x^5 - \cdots + 945x^{41}-45x^{43}+x^{45} = N$?

Limit of the sequence $a_{n+1}=\frac{1}{2} (a_n+\sqrt{\frac{a_n^2+b_n^2}{2}})$ - can't recognize the pattern

How to compute $\int_0^1\frac{\text{Li}_2(x^2)\arcsin^2(x)}{x}dx$ or $\sum_{n=1}^\infty\frac{4^nH_n}{n^4{2n\choose n}}$

Interesting infinite nested square roots of 2 for $2\cos1°$ and $2\sin1°$

Find the Maximum Trigonometric polynomial coefficient $A_{k}$

In deriving the catenary equation, how does integrating $\frac{dy'}{\sqrt{1+(y')^2}}=\frac1a dx$ yield $\sinh^{-1}(y')=\frac{x}{a}$?

How to find finite trigonometric products [closed]

When does $a \cdot\sin(x) = \sin(a \cdot x)$?

Prove trig identity: $\tan(x) + \cot(x) = \sec(x) \csc(x)$ wherever defined

$\sum_{i=1}^{89} \sin^{2n} (\frac{\pi}{180}i)$ is a dyadic rational

Evaluate $\int\frac {\csc^2{x}-2005}{\cos^{2005}{x}} dx $

solve $\frac{\sqrt{5}(\cos \theta - \sin \theta)}{3\sqrt{2}}=\tan \theta$

Are there polynomials in $\mathbb{R}[x]$, other than $P(x)=x^2$, such that $P(\sin x)+P(\cos x)=1$ for all real $x$?