(a/sin(A)) = (b/sin(B)) = (c/sin(C)) = 2r
sin(½A) = ((s-b)(s-c)/bc)^½       s=½(a+b+c)
cos(½A) = (s(s-a)/bc)^½       s=½(a+b+c)
tan(½A) = ((s-b)(s-c)/(s(s-a)))^½       s=½(a+b+c)
tan(½(B-C)) = ((b-a)/(b+c))cot(½A)
sin(-A) = -sin(A)
cos(-A) = cos(A)
cosec(A) = 1/sin(A)
sec(A) = 1/cos(A)
cot(A) = 1/tan(A)
sin²(A) + cos²(A) = 1
cos²(A) = (1 + cos(2A))/2
sin²(A) = (1 - cos(2A))/2
sin(A)cos(A) = (sin(2A))/2 sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
sin(A-B) = sin(A)cos(B) - cos(A)sin(B)
cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
cos(A-B) = cos(A)cos(B) + sin(A)sin(B)
sec²(A) = 1 + tan²(A)
cosec²(A) = 1 + cot²(A)
sin(2A) = 2sin(A)cos(A)
cos(2A) = 2cos²(A) - 1
cos(2A) = 1 - 2sin²(A)
tan(2A) = (2tan(A))/(1-tan²(A))
tan(A+B) = (tan(A)+tan(B))/(1-tan(A)tan(B))
tan(A-B) = (tan(A)-tan(B))/(1+tan(A)tan(B))
sin(3A) = 3sin(A)-4sin³(A)
cos(3A) = 4cos³(A)-3cos(A)
tan(3A) = (3tan(A)-tan³(A))/(1-3tan²(A))
sin(2A) = 2tan(A)/(1+tan²(A))
cos(2A) = (1-tan²(A))/(1+tan²(A))
sin(A)+sin(B) = 2sin(½(A+B))cos(½(A-B))
sin(A)-sin(B) = 2cos(½(A+B))sin(½(A-B))
cos(A)+cos(B) = 2cos(½(A+B))cos(½(A-B))
cos(A)-cos(B) = 2sin(½(A+B))sin(½(B-A))
tan(A)+tan(B) = sin(A+B)/(cos(A)cos(B))
tan(A)-tan(B) = sin(A-B)/(cos(A)cos(B))
cos(A+B)+cos(A-B) = 2cos(A)cos(B)
cos(A-B)-cos(A+B) = 2sin(A)sin(B)
sinh(x) = (e^x-e^-x) / 2
cosh(x) = (e^x+e^-x) / 2
tanh(x) = (e^x-e^-x) / (e^x+e^-x)
sin(x) = (x¹/1!) - (x³/3!) + (x⁵/5!) - ...
cos(x) = (x⁰/0!) - (x²/2!) + (x⁴/4!) - ...
e^x = (x⁰/0!) + (x¹/1!) + (x²/2!) + ...
sinh(x) = (x¹/1!) + (x³/3!) + (x⁵/5!) + ...
cosh(x) = (x⁰/0!) + (x²/2!) + (x⁴/4!) + ...
log(1+x) = (x¹/1!) + (x²/2!) + (x³/3!) + ...
(x+1)ⁿ = 1 + (nx¹/1!) + (n(n-1)x²/2!) + (n(n-1)(n-2)x³/3!) + ...
sin(x) = cos(x)
cos(x) = -sin(x)
tan(x) = sec²(x)
cot(x) = -cosec²(x)
sec(x) = sec(x)tan(x)
cosec(x) = -cosec(x)cot(x)
sinh(x) = cosh(x)
cosh(x) = sinh(x)
tanh(x) = sech²(x)
cosech(x) = -coth(x)cosech(x)
sech(x) = -tanh(x)sech(x)
coth(x) = -cosech²(x)
axⁿ = anx^(x-1)
e^ax = ae^ax
a^x = a^xlog_e(a)
x^x = x^x/(1+log_e(x))
log_e(x) = 1/x
log_a(x) = 1/(x log_a(e))
sin^-1(x/a) = 1/(a²-x²)^½
cos^-1(x/a) = -1/(a²-x²)^½
tan^-1(x/a) = a/(a²+x²)
e^ax = ae^ax
∫xⁿ = x⁽ⁿ⁺¹⁾/(n+1) +c
∫1/(x²+n²) =(1/n) tan^-1(x/n) +c
∫1/(x²-n²) =(1/2n)log_e((x-n)/(x+n)) +c
∫1/(a+bx) = 1/(b log_e(a+bx)) +c
∫x/(ax+b) = (ax + (1-log_e(ax+b))b)/a² +c
∫1/x =log_e(x) +c
∫1/(x²-a²)^½ = cosh^-1(x/a) +c
∫1/(x²+a²)^½ = sinh^-1(x/a) +c
∫e^x = e^x +c
∫1/(a²-x²) = (1/a) tanh^-1(x/a) +c
∫a^x = a^x/log_e(a) +c
∫xa^x = (a^x/log_e(a))-(a^x/(log_e(a))²) +c
∫xe^ax = (e^ax(ax-1))/a² +c
∫log_e(x) = x(log_e(x)-1) +c
∫1/xlog_e(x) =log_e(log_e(x) ) +c
∫sin(x) = -cos(x) +c
∫cos(x) = sin(x) +c
∫tan(x) = -log_e(cos(x)) +c
∫cotan(x) =log_e(sin(x)) +c
∫sec(x) =log_e(sec(x) + tan(x)) +c
∫cosec(x) = log_e(tan(x/2)) +c
∫sinh(x) = cosh(x) +c
∫cosh(x) = sinh(x) +c
∫tanh(x) = log_e(cosh(x)) +c
∫cosech(x) =log_e(tanh(x/s)) +c
∫sech(x) = tan^-1(sinh(x)) +c
∫coth(x) =log_e(sinh(x))
∫sinh²(x) = (-x/2) + (sinh(2x)/4) +c
∫cosh²(x) = (x/2) + (sinh(2x)/4) +c
∫sech²(x) = tanh(x) +c
∫cosech²(x) = -coth(x) +c
∫tanh²(x) = x - tanh(x) +c
∫anx^(n-1) = axⁿ +c
∫ae^ax = e^ax +c
∫a(cos(ax)) = sin(ax) +c
∫a(sin(ax)) = -cos(ax) +c
∫a(sec²(ax)) = tan(ax) +c
∫1/(1-x²)^½ = sin^-1(x) +c
∫1/(1+x²) = tan^-1(x)
x²+y²+2ax+2by+c = 0     O=(-a, -b)     r=(a²+b²-c)^½
(x²/a²)+(y²/b²) = 1
y = x²+mx+c
y = mx+c
x³+y³ = (x+y)(x²-xy+y²)
x³-y³ = (x-y)(x²+xy+y²)
x = (-b±(b²-4ac)^½)/2a
log_e(xy) = log_e(x)+log_e(y)
log_e(x/y) = log_e(x)-log_e(y)
log_e(x^y) = y(log_e(x))
(log_e(x))(log_x(e)) = 1
log_e(x) = (log_a(x))(log_e(a))
i = (-1)^½
a²+b²=c²
a^x a^y=a^x+y
e^ix=cos(x)+i sin(x)
r(cos(x)+i sin(x))^y=r^y(cos(yx)+i sin(yx))
∑x=n(n+1)/2
∑x²=n(n+1)(2n+1)/6
∑x³=n²(n+1)²/4