Intereting Posts

Hint on an exercise of Mathieu groups
Triangle inequality for subtraction?
How prove that $\frac{1}{\sin^2\frac{\pi}{2n}}+\frac{1}{\sin^2\frac{2\pi}{2n}}+\cdots+\frac{1}{\sin^2\frac{(n-1)\pi}{2n}} =\frac{2}{3}(n-1)(n+1)$
Monotone class theorem vs Dynkin $\pi-\lambda$ theorem
How to integrate this type of fractions
How do I acquire an intuitive understanding of the distributive law over a disjunction?
A continuous mapping with the unbounded image of the unit ball in an infinite-dimensional Banach space
How to calculate probability using multinomial distribution?
What are some algebraically closed fields?
What is the *middle* digit of $3^{100000}$?
Representation of quiver $1 \to 2 \to 3$
Endomorphisms of forgetful functor $\mathbf{Grp}\to \mathbf{Set}$
Prerequisite to start learning Topological K-Theory
Function example? Continuous everywhere, differentiable nowhere
Two questions with respect to the determinants

Possible Duplicate:

infinite product of sine function

Here is an other one which is more or less what Euler did in one of his proofs.

The function sinx where x∈R is zero exactly at x=nπ for each integer n. If we factorized it as an infinite product we get

- Why is $\cos(x)^2$ written as $\cos^2(x)$?
- Maximum area of a triangle
- Why is $\arctan(x)=x-x^3/3+x^5/5-x^7/7+\dots$?
- How to calculate $\left( 1+\tan 5^\circ\right) \left( 1+\tan 10^\circ\right)\left( 1+\tan 15^\circ\right)\cdots\left( 1+\tan 40^\circ\right)$
- What are functions used for?
- Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$

How to prove

$$

\sin x=…(1+\frac{x}{3\pi})(1+\frac{x}{2\pi})(1+\frac{x}{\pi})x(1-\frac{x}{3\pi})(1-\frac{x}{2\pi})(1-\frac{x}{\pi})…

$$

- A question about the arctangent addition formula.
- Constructing a new function
- Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$
- What is wrong with my integral? $\sin^5 x\cos^3 x$
- Minimum value of $2^{\sin^2x}+2^{\cos^2x}$
- Which trigonometric identities involve trigonometric functions?
- Equation of sine wave around a circle
- Is there a way to calculate $\displaystyle \sum_{k=0}^{n}\sin({2^kx})$?
- Radius of circle by knowing a cross section.
- Verifing $\int_0^{\pi}x\ln(\sin x)\,dx=-\ln(2){\pi}^2/2$

Courtesy of Edmund Landau, from his Differential and Integral Calculus.

- On matrix norm equivalence
- A triangular representation for the divisor summatory function, $D(x)$
- Can every set be expressed as the union of a chain of sets of lesser cardinality?
- Partitioning $$ into pairwise disjoint nondegenerate closed intervals
- The annihilator of an intersection is the sum of annihilators
- How many maximum number of isosceles triangle are possible in a regular polygon of $n$ sides?
- A question on $p$-groups, and order of its commutator subgroup.
- Blackboard bold, Bold, Fraktur, and Reserved Variable.
- Prove that $ f$ is uniformly continuous
- Compute the definite integral
- Problem on ultrafilters
- For $x>0$, $x + \frac1x \ge 2$ and equality holds if and only if $x=1$
- Subtracting a constant from log-concave function preserves log-concavity, if the difference is positive
- Continuity of Fixed Point
- a non-monotonic function on with infinitely many points of discontinuity such that the function is bounded & Riemann integrable on .