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math_formulas

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\tan(2 x) = \frac{\sin(x \cdot 2)}{\cos(x \cdot 2)}

(-1) + x * x = (x + (-1))*(x + 1)

((-1)\cdot (-1))^{1 / 2} = \left((-1) \cdot (-1)\right)^{\frac{1}{2}} = |-1| = 1

s\cdot i\cdot x\cdot 2\cdot \frac12\cdot r = s\cdot r\cdot i\cdot x

0 = n^2 + 5 \cdot n + 12 \cdot (-1) \Rightarrow n^3 = 60 \cdot (-1) + n \cdot 37

8*6*5 = 240

8 + 2 \cdot y = 104 \Rightarrow y = \frac12 \cdot (104 + 8 \cdot \left(-1\right)) = 48

\left(y + 2\right) \cdot (y + 3) = 6 + y^2 + 5 \cdot y

t_i \cdot t_i = t_i^2\cdot \frac33

5 + z*2 = 2z + 2 + 3

Q - z = j \cdot s \Rightarrow j = \frac1s \cdot (-z + Q)

\frac{1}{x + 2} \cdot \left(2 \cdot x^4 + 1\right) = 0 + \tfrac{2 \cdot x^4 + 1}{x + 2}

\left(1 + m\right)! = \left(m + 1\right) \cdot m \cdot (m + (-1)) \cdot \left(2 \cdot (-1) + m\right) \cdot ... \cdot 2

d^g = \frac{1}{d^{-g}}

\dfrac{6q}{12q^2} = \dfrac{6}{12} \cdot \dfrac{q}{q^2}

\cos(-\theta\times 2 + \frac{\pi}{2}) = \sin(2\times \theta)

(2 \cdot (-1) + y) \cdot (y + 2) = 4 \cdot \left(-1\right) + y^2

a*g = 1/(\dfrac{1}{a*g}) = \frac{1}{1/a*1/g} = 1/(\frac{1}{g}*1/a) = g*a

|y + (-1)| = |1 - y| \geq |1| - |y| = 1 - |y| rightarrow 3/4 \leq |y|

-\frac{1}{k + 1}\cdot \frac{1}{2} + \dfrac{1}{k + (-1)}\cdot 1/2 = \frac{1}{((-1) + k)\cdot (1 + k)}

\frac{76.7}{100} = 0.767

\frac{1}{5}\cdot 300\cdot 3 = 180

|y_1|/|y_2| = |\frac{1}{y_2}\cdot y_1|

\pi/2 + \pi/4 = \pi \cdot 3/4

(z - y)\cdot (z^{\left(-1\right) + n} + \dots + y^{n + (-1)}) = z^n - y^n

1 + x = \frac{1}{x}\left(x + x^2\right)

A\cdot D = B\cdot D rightarrow A\cdot B = 2\cdot A\cdot D

\tfrac{z_n}{1 + z_n} = 1 - \tfrac{1}{1 + z_n}

\frac{1}{3}\pi + \frac{7}{4}\pi = \frac{25}{12}\pi

\frac{90*(-1) + n*9}{9 - 63*n} = 9/9*\frac{10*(-1) + n}{-n*7 + 1}

-\frac{10}{15 + q \cdot 9} \cdot 4/4 = -\frac{40}{60 + 36 \cdot q}

a \times a - b^2 = (a + b)\times \left(a - b\right)

2 \cdot 999 = 1998

\frac18\cdot 3\cdot \frac{4}{9} = \frac16

2\sqrt{3}/3 = 2/(\sqrt{3})

52\cdot 144 + 144^2 = 168^2

\sin{6*x}/2 = \sin{x*3}*\cos{x*3}

\frac1w = (M\cdot x + l\cdot w)/w = M\cdot x/w + l

|a_n - a_{n + k} + b_n - b_{k + n}| = |a_n + b_n - b_{k + n} + a_{n + k}|

1/B = Z \cdot C \implies \frac{1}{Z \cdot B} = C

2.03 \cdot 10 = \frac{2.03}{1000} \cdot 10 = \frac{1}{100} \cdot 2.03

2\cdot 3\cdot 5\cdot 7 = 210

4 \cdot x^2 = (2 \cdot x)^2 = 2 \cdot 2 \cdot x \cdot x

\sqrt{-x^2 + 1} = \sin(\arccos{x})

2^{5/12} = 1.334839\cdot \dots \approx 4/3

3\tan^2(x) = -3 + 3\sec^2(x)

\mathbb{E}[W_1] + \mathbb{E}[W_2] + \dots + \mathbb{E}[W_f] = \mathbb{E}[W_1 + W_2 + \dots + W_f]

\operatorname{acos}\left(\cos{0}\right) = \operatorname{acos}(\cos{\pi*2})

16/3 = -\dfrac23*((1 + (-1))^3 - \left(1 + 1\right) * (1 + 1)^2)

-s*2*2*5 = -s*20

4 \times (k + 1) \times (k + 1) + (-1) = (2 \times k + 1) \times \left(2 \times k + 3\right) = \left(2 \times k + 1\right) \times (2 \times (k + 1) + 1)

\frac{1}{\frac{1}{\frac{1}{\frac{1}{25}}}} = 5^{-2(-(-1) (-1))} = 5^2 = 25

j \cdot j^2 + 3 \cdot j^2 + 3 \cdot j + 1 = (j + 1)^3

((-1) \cdot (-1))^{\frac{1}{2}} = ((-1)^2)^{\dfrac{1}{2}} = |-1| = 1

S \cdot X = S \cdot X

24/23 = 1 + \frac{1}{23}

\pi\cdot 9/4 = \pi \tfrac{1}{12}11 + \pi \frac{1}{3}4

4 = 2 t t\cdot (1 - 1/7) = 12/7 t^2

2*x - x^2 = 1 - ((-1) + x)^2 \Rightarrow \sqrt{1 - (x + (-1))^2} = \sqrt{2*x - x^2}

\tfrac{1}{-x + (x^2 + 1)^{1/2}} = (x \cdot x + 1)^{1/2} + x

(h - (g \times h \times 2)^{1/2} + g) \times (h + (g \times h \times 2)^{1/2} + g) = g \times g + h^2

x + z = -1 \implies z \cdot x = -2004

\frac{q \cdot 28 + 4}{28 \cdot \left(-1\right) - 12 \cdot q} = \frac{1 + 7 \cdot q}{7 \cdot \left(-1\right) - q \cdot 3} \cdot 4/4

176^{1 / 2} + 44^{\frac{1}{2}} = (16*11)^{1 / 2} + \left(4*11\right)^{1 / 2}

\mathbb{E}(X) = 0 \Rightarrow \mathbb{E}(X^2) = 0

1 + 2^{10500} + 2^{5251} = (1 + 2^{5250}) \cdot (1 + 2^{5250})

(z_2 + z_1)^2 = z_2^2 + 2z_2 z_1 + z_1^2

21\times 2/(21\times 3) = \tfrac{1}{63}\times 42

2/12 \cdot \dfrac{4}{11} = 2/33

8 = 50*(-1) + 58

\tfrac{z^2}{2*(-1) + z} = z + 2 + \frac{1}{z + 2*(-1)}*4

39 = \left(-1\right) + 10\times 4

\frac{E \cdot L}{A \cdot E} = \tan(A \cdot E \cdot L) rightarrow \arctan(\frac{E \cdot L}{E \cdot A}) = L \cdot A \cdot E

-20/54 = \frac{(-20)*1/2}{54*\frac12} = -10/27

(1 + k)^3 - k^3 = 3 \cdot k^2 + k \cdot 3 + 1

e^{10*\frac{11*i*\pi}{12}} = (e^{\frac{11*\pi*i}{12}})^{10}

\frac144*\frac{3}{3z + 2} = \frac{1}{12 z + 8}12

2\cdot 1+2\cdot 4+2\cdot 9=28

-\pi\cdot \frac34 = -\tfrac{19}{12}\cdot \pi + \frac56\cdot \pi

1638 = 2*3^2*7*13 = (1^2 + 1^2)*3^2 (2^2 + 1^2 + 1^2 + 1^2) \left(3^2 + 2^2\right)

|z^2 + 1| = z \cdot z + 1 = |z|^2 + 1

w_2 F = -iw_1 F \Rightarrow Fw_2 = Fw_1 = 0

\binom{r + 3}{r} = \binom{r + 3}{3} = (r + 1)*\left(r + 2\right)*(r + 3)/3!

\left(\binom{21}{4} + \binom{20}{4}\right)*60 = 5*4*3*\binom{21}{4} + \binom{20}{4}*\binom{3}{2}*5*4

c^{x + 1} \coloneqq c\cdot c^x

{2\cdot x \choose x + (-1)} = \frac{(2\cdot x)!}{(x + (-1))!\cdot (x + 1)!} = \frac{1}{x + 1}\cdot x\cdot {2\cdot x \choose x}

(\psi + (-1)) \cdot (\psi + (-1)) + 1 \cdot 1 = \psi^2 - 2\psi + 2

(6^{\frac{1}{2}} + 3)/6 = \frac{1}{6} \cdot 6^{1 / 2} + 1/2

\frac{1}{(x + 1)*2} + \frac{1}{2*(-x + 1)} = \tfrac{1}{1 - x^2}

(z^2 + v^2) \cdot (x^2 + y^2) = (z \cdot x + v \cdot y) \cdot (z \cdot x + v \cdot y) + (-z \cdot y + v \cdot x) \cdot (-z \cdot y + v \cdot x)

7^2 + 7\cdot 11 + 11 \cdot 11 = 13\cdot \left(2^2 + 2\cdot 3 + 3^2\right) = 13\cdot 19

(y + 3\cdot (-1))\cdot (4\cdot (-1) + y)\cdot (y + 5\cdot (-1)) = 60\cdot \left(-1\right) + y^3 - 12\cdot y \cdot y + 47\cdot y

\frac{4}{10} = \dfrac{2}{5}

{-1/2 \choose 2} = \frac{1}{8}\cdot 3

-{31 \choose 2}\cdot {3 \choose 1} + {82 \choose 2} = 1926

\left(1 + y\right) (y + \left(-1\right)) = \left(-1\right) + y * y

\frac{40}{36} \cdot \frac{x^2}{x^3} = \dfrac{40 \cdot x^2}{36 \cdot x^3}

\tan^2(\pi/6) = \dfrac{1}{3}

5\cdot 1/3/(\frac13\cdot 2) = \dfrac{1}{3}\cdot 5\cdot \frac{3}{2}

\theta^2 \theta^2 = \theta \theta^3 = 3\theta^2 - \theta