Can you prove this?

0.999

>>8939945
-1/12

>>8939929
hmmm...

I define Aleph-pepe as being the answer to this question.

>>8939929
of what use is your marvelous proof since pi does not exist?

[eqn] \sin \frac{\pi}{7} = \sin \frac{6\pi}{7} [/eqn]

Using the trigonometry identity:
[eqn] \sin 7 \theta = 7 \sin \theta - 56 \sin^3 \theta + 112 \sin^5 \theta - 64 \sin^7 \theta = 0 [/eqn]

[eqn] 64 \sin^6 \theta - 112 \sin^4 \theta + 56 \sin^2 \theta - 7 = 0 [/eqn]
[eqn] \sin 7 \theta = 0 [/eqn]
[eqn] \theta = \frac{2k\pi}{7} , k=1,2,3,4,5 and 6 [/eqn]

The sum of the roots of the equation is:
[eqn] \sin \frac{2\pi}{7} + \sin \frac{4\pi}{7} + \sin \frac{6\pi}{7} + \sin \frac{8\pi}{7} + \sin \frac{10\pi}{7} + \sin \frac{12\pi}{7} = 0 [/eqn]

And I'm too dumb to continue any further.

>>8940082
[eqn] \sin \frac{\pi}{7} = \sin \frac{6\pi}{7} [/eqn]

Using the trigonometry identity:
[eqn] \sin 7 \theta = 7 \sin \theta - 56 \sin^3 \theta + 112 \sin^5 \theta - 64 \sin^7 \theta [/eqn]

[eqn] 64 \sin^6 \theta - 112 \sin^4 \theta + 56 \sin^2 \theta - 7 = 0 [/eqn]
[eqn] \sin 7 \theta = 0 [/eqn]
[eqn] \theta = \frac{2k\pi}{7} , k=1,2,3,4,5~and~6 [/eqn]

The sum of the roots of the equation is:
[eqn] \sin \frac{2\pi}{7} + \sin \frac{4\pi}{7} + \sin \frac{6\pi}{7} + \sin \frac{8\pi}{7} + \sin \frac{10\pi}{7} + \sin \frac{12\pi}{7} = 0 [/eqn]

I'm really retarded at using LaTeX.

>>8939929
Use a calculator

File: file.png (54KB, 1339x520px) Image search: [Google]

54KB, 1339x520px

>>8939929
WRONG

>>8939929
No, because it is a false statement. The correct identity is cot(pi/7) + cot(2pi/7)+cot(4pi/7) = sqrt(7).

if 9.58 = 328, then
9.0 = ???

>>8940088
As stated in the thread, the identity is wrong, but to continue your calculation you could note that the polynomial [eqn]f(x)=x^n+ b_{n-1}x^{n-1}+...+b_1 x+b_0=(x-a_1)(x-a_2)\cdot ...\cdot (x-a_n)[/eqn]
has as roots the [math]a_i[/math], and that [math]a_1+a_2+...+a_n =-b_{n-1}[/math], so that the transformation [math]x\mapsto\frac{1}{y}[/math] creates a polynomial ( once made monic) whose [math]y^{n-1}[/math] coefficient, say [math]-c_{n-1}=\frac{1}{a_1}+...+\frac{1}{a_n}[/math]

>>8941510
9.58 is not equal to 328 dumbfuck

File: proof.jpg (136KB, 1600x943px) Image search: [Google]

136KB, 1600x943px

>>8940044
Then how do you explain this?