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ddrg
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math_formulas

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12,721
\cos(b + x) = -\sin(b)\cdot \sin\left(x\right) + \cos(b)\cdot \cos(x)
24,762
(-\sin(A) + 1)*\left(\sin(A) + 1\right) = \cos^2(A)
-21,604
0 = \cos(\frac12\times 3\times \pi)
28,804
r^{x + X} = r^X*r^x
-6,685
\frac{4}{10} + \frac{5}{100} = 40/100 + 5/100
15,997
A - B = 0 \Rightarrow 0 = A \cdot A - B^2
4,138
\frac{1}{x + (-1)}*(3*\left(-1\right) + x^3 + x^2 + x) = x^2 + 2*x + 3
27,728
h*h*g*g = h*g*h*g
5,366
-10 = \frac{6}{7*h} \Rightarrow h = -\frac{70}{6}
1,193
n = m*5 + 4\Longrightarrow n = 8*3 + 5*(m + 4*\left(-1\right))
19,491
-(b - c) \cdot 3 = \left(c + a + b\right) \cdot (-c + b) \Rightarrow c + a + b = -3
1,611
1/10 = \dfrac{1}{8}\cdot 4 / 5
-20,767
\frac{4}{5 + t}\cdot \dfrac13\cdot 3 = \frac{12}{3\cdot t + 15}
17,590
(-\sqrt{2} + x)\cdot (x + \sqrt{2}) = 2\cdot (-1) + x^2
34,920
(-4)^{1/2} = 4^{1/2}*\left(-1\right)^{1/2} = 2*i
23,184
\frac{1}{6} \cdot 5 \cdot T + 8/9 \cdot 3 \cdot T = \frac{1}{6} \cdot 5 \cdot T + 16/6 \cdot T = \dfrac{1}{2 \cdot T} \cdot 7
23,321
g^m*g * g = g^{m + 2} = g^2*g^m
40,660
188 = 9\cdot 4\cdot 3 + 4\cdot 2 + 12\cdot 3\cdot 2
-4,795
30.5*10^4 = 10^{1 + 3}*30.5
6,135
(y + 4)*(2 + y) = y^2 + 6*y + 8
-17,518
31 = 42\cdot (-1) + 73
756
\cosh(y) = \left(e^y + e^{-y}\right)/2 \leq e^{y \cdot y/2}
13,897
t = \frac{-t^3 + t*3}{1 - 3 t^2} + 2 \Rightarrow \left(t + 2 (-1)\right) \left(1 - 3 t^2\right) = -t^3 + 3 t
-1,795
\dfrac{1}{12}\cdot 7\cdot \pi + \frac{\pi}{2} = \pi\cdot \frac{13}{12}
18,240
-1 = (-1)^{2 \cdot \dfrac12 \cdot 3} = ((-1)^2)^{3/2} = 1^{3/2} = 1^{1/2}
25,815
3 \cdot (x^2 + z^2)^2 \cdot \left(2 \cdot x \cdot x' + z \cdot 2\right) = 2 \cdot (x^2 - z^2) \cdot (2 \cdot x \cdot x' - 2 \cdot z)
20,020
\frac{1}{z x} = \frac{1}{z x}
3,622
(\operatorname{acos}(0) - \operatorname{acos}\left(1\right))/2 = \frac{\pi}{4}
34,124
\sqrt{5}/2 + \frac{1}{2} = (1 + \sqrt{5})/2
21,926
p\cdot y^{(-1) + p} = \frac{\partial}{\partial y} y^p
18,944
r^2 + 2 \cdot r + 4 \cdot \left(-1\right) = 0 \Rightarrow -1 \pm \sqrt{5} = r
13,319
1^2 + 22^2 + 5^2 + 4^2 = 526
27,927
(5 - \sqrt{23})*(5 + \sqrt{23}) = 2
11,356
\tfrac{1}{n^2}\cdot n^{1/2} = \frac{1}{n^{\frac32}}
30,431
1 + 12 \times \left(6 + (-1)\right) = 61
36,950
(U_2 + U_1) Z = ZU_2 + ZU_1
20,040
(X + (-1))*((-t + 1)*X^2 - X*t - t) = t + X^3*(-t + 1) - X^2
-3,176
\sqrt{11} \cdot \sqrt{4} + \sqrt{11} = \sqrt{11} + \sqrt{11} \cdot 2
-22,805
\frac{1}{48} \cdot 60 = \frac{12}{4 \cdot 12} \cdot 5
8,534
3 * 3*2 * 2*5*7 = 1260
7,576
568 = 8 + 10\cdot 56
8,927
2 + A\cdot 4 = l \Rightarrow 3\cdot l + 2 = 12\cdot A + 8 = 4\cdot (3\cdot A + 2)
19,325
(1/4)^2 + \left(1/2\right)^2 + (1/4) \cdot (1/4) = \frac183 = 0.375
-29,343
f_2^2 - f_1^2 = (f_2 - f_1) (f_2 + f_1)
-1,344
\frac{1}{1/8\cdot (-7)}\cdot (\frac13\cdot \left(-5\right)) = -\dfrac{5}{3}\cdot (-\frac{8}{7})
21,931
e - q \cdot b = s \implies e = b \cdot q + s
18,918
\dfrac{2 \cdot z^2}{z^2 + \left(-1\right)} = 2 + \frac{1}{z^2 + (-1)} \cdot (z + 1 - z + (-1)) = 2 + \frac{1}{z + \left(-1\right)} - \frac{1}{z + 1}
22,620
(-h + a) \cdot (a^{k + (-1)} + h \cdot a^{2 \cdot (-1) + k} + h^2 \cdot a^{3 \cdot (-1) + k} + \ldots + h^{k + 3 \cdot (-1)} \cdot a \cdot a + h^{2 \cdot (-1) + k} \cdot a + h^{k + (-1)}) = a^k - h^k
14,658
x/r_1 \cdot k = \frac{k}{\pi \cdot r_1 \cdot 2} \cdot \pi \cdot x \cdot 2
10,916
\frac{1989}{867} = \frac{1989}{51 \cdot 17} \cdot 1 = \frac{1}{17} \cdot 39
49,149
68=4*17
35,823
{100 \choose 48} = {100 \choose 52} = {100 \choose 50}*\dfrac{50}{51*52}*49
16,637
A a' = 1\Longrightarrow 1/a' = A
29,846
k/a = \dfrac{a}{a + k} rightarrow k \cdot k + k\cdot a = a^2
23,616
\left(45 = 8\cdot x + x \Rightarrow 45 = 9\cdot x\right) \Rightarrow 5 = x
8,436
E \times H = H \times H \times H = H^3 = H \times H^2 = H \times E
25,068
\frac12 = 0 + \frac{1}{4} + 1/8 + \cdots
17,947
n_1 + (-1) + \ldots + n_t + \left(-1\right) = n_1 + \ldots + n_t - t
13,101
d = f \implies 0 = -f + d
-1,836
\pi*13/12 + \pi*3/4 = \pi \frac1611
-22,262
3 \cdot \left(-1\right) + x \cdot x + 2 \cdot x = (3 + x) \cdot (x + (-1))
14,138
\frac{1}{2*k*2^k}*2^{k*2} = \dfrac{2^k}{2*k}
12,236
3 + m \cdot 6 = (2 \cdot m + 1) \cdot 3
10,776
(5 - \sqrt{6}\cdot 2) \left(5 + 2 \sqrt{6}\right) = 1
-10,818
\frac{1}{13} \cdot 52 = 4
6,899
\mathbb{E}(\bar{B})^2 + \mathbb{Var}(\bar{B}) = \mathbb{E}(\bar{B}^2)
32,800
-z*9*z = -9*z^2
30,895
\frac{π}{2 \cdot 2^{1/2}} = \frac{π}{4} \cdot 2^{1/2}
21,900
X + 2/3\cdot (x^{\frac12})^3 = X + \dfrac13\cdot 2\cdot x^{3/2}
14,360
|x - h| + |h - f| = -(x - h) + h - f = -x + 2 \cdot h - f
-10,490
\frac{18}{3 \times c} = 6/c \times \dfrac33
34,118
x \cdot L = L^1 \cdot x
7,557
U + x + W = U + x + W
4,867
(19\cdot (-1) + p^2)\cdot (p^2 + (-1)) = p^4 - 20\cdot p^2 + 19
3,051
2 > u - y \Rightarrow u + 2\cdot \left(-1\right) \lt y
-19,793
-1.325 = -\tfrac{53}{40}
-20,806
-\dfrac{9}{7} \cdot \frac{y + 3 \cdot (-1)}{3 \cdot (-1) + y} = \dfrac{-9 \cdot y + 27}{y \cdot 7 + 21 \cdot (-1)}
6,633
2*k = -k + 3*k
16,339
r \cdot (m + n - r) = (-r + m) \cdot r + \left(-r + n\right) \cdot r + r \cdot r
31,942
(3 \cdot 7 \cdot 11 \cdot 13) \cdot (3 \cdot 7 \cdot 11 \cdot 13) \cdot 21737 = 196024461633
23,299
1562500 = 5^8\cdot 4
15,360
4*k + 4 = k*4 + 4
-13,870
10\times (3 + 1) = 10\times 4 = 40
28,522
-(x \cdot x - 4 \cdot x + 5 \cdot (-1)) = -x \cdot x + 5 + 4 \cdot x
35,922
0 + i c = i c
22,723
n\cdot 2 + 1 = \left(n + 1\right)^2 - n^2
16,523
G^c \cap (X \cap Y^c) = X \cap (G^c \cap Y^c) = X \cap G \cup Y^c
9,498
\left|{A*A^T}\right| = \left|{A*A^T}\right|
14,975
\left(f + h\right)*(f + h) = f*f + 2*f*h + h*h
21,158
\frac{\partial}{\partial x} (h*x) = \frac{\partial}{\partial x} \left(h*x\right)
-16,591
2\sqrt{112} = 2\sqrt{16 \cdot 7}
-3,884
\dfrac{3}{9x^5}x^2 = \frac{1}{x^5}x * x \dfrac{3}{9}
4,393
5^3 \cdot \binom{5}{3} \cdot 5^2 = 31250
32,244
3*\left(h + x\right) = x*3 + 3*h
33,285
\frac{1}{5}\cdot 2 = \frac15\cdot 2
8,589
(m + (-1))\cdot (m^4 + m^3 + m^2 + m + 1) = m^5 + (-1)
20,860
h \cdot h + d^2 + c \cdot c = (h + d + c) \cdot (h + d + c) - 2\cdot (h\cdot d + d\cdot c + c\cdot h) = -2\cdot (h\cdot d + d\cdot c + c\cdot h)
-25,245
-\frac{1}{2^5}\cdot 4 = -4/32 = -\frac{1}{8}
33,671
\left\lceil{\frac{1}{3 (-1) + \pi}}\right\rceil = 8
7,829
\pi/180 \cdot x \cdot 180/\pi = x