Hyperbolic Trig Identities

Hyperbolic Trig Identities is like trigonometric identities yet may contrast to it in specific terms. The fundamental hyperbolic functions are hyperbola sin and hyperbola cosine from which the other trigonometric functions are inferred. You can easily explore many other Trig Identities on this website.

So here we have given a Hyperbola diagram along these lines giving you thought regarding the places of sine, cosine, and so on.

Hyperbolic Trig Identities

Various Essential Hyperbolic Trig Identities

Introduction

  • x and y are independent variables.
  • e is the base of the natural logarithm.
  • d is the differential operator.
  • int is the integral symbol.
  • C is the constant of integration.

Hyperbolic Trig Identities

sinh x = (ex – ex)/2Equation 1
cosh x = (ex + ex)/2Equation 2
sech x = 1/cosh xEquation 3
csch x = 1/sinh xEquation 4
tanh x = sinh x/cosh xEquation 5
coth x = 1/tanh xEquation 6
cosh2 x – sinh2 x = 1Equation 7
tanh2 x + sech2 x = 1Equation 8
coth2 x – csch2 x = 1Equation 9
sinh (x + y) = sinh x cosh y + cosh x sinh yEquation 10
sinh (x – y) = sinh x cosh y – cosh x sinh yEquation 11
cosh (x + y) = cosh x cosh y + sinh x sinh yEquation 12
cosh (x – y) = cosh x cosh y – sinh x sinh yEquation 13
sinh2 x = [-1 + cosh (2 x)]/2Equation 14
sinh (2 x) = 2 sinh x cosh xEquation 15
cosh2 x = [1 + cosh (2 x)]/2Equation 16
cosh (2 x) = cosh2 x + sinh2 xEquation 17
arcsinh x = ln [x + (x2 + 1)1/2]Equation 18
arccosh x = ln [x + (x2 – 1)1/2]Equation 19
arctanh x = (1/2) ln [(1 + x)/(1 – x)]Equation 20
arccoth x = (1/2) ln [(x + 1)/(x – 1)]Equation 21
arcsech x = ln [[1 + (1 – x2)1/2]/x]Equation 22
arccsch x = ln [[1 + (1 + x2)1/2]/|x|]Equation 23
tanh (2 x) = 2 tanh x/(1 + tanh2 x)Equation 24
coth x – tanh x = 2 csch (2 x)Equation 25
coth x + tanh x = 2 coth (2 x)Equation 26
(d/dx) sinh x = cosh xEquation 27
(d/dx) cosh x = sinh xEquation 28
(d/dx) tanh x = sech2 xEquation 29
(d/dx) coth x = -csch2 xEquation 30
(d/dx) sech x = -sech x tanh xEquation 31
(d/dx) csch x = -csch x coth xEquation 32
(d/dx) arcsinh x = 1/(x2 + 1)1/2Equation 33
(d/dx) arccosh x = 1/(x2 – 1)1/2Equation 34
(d/dx) arctanh x = 1/(1 – x2)Equation 35
(d/dx) arccoth x = 1/(1 – x2)Equation 36
(d/dx) arcsech x = -1/[x (1 – x2)1/2]Equation 37
(d/dx) arccsch x = -1/[|x| (1 + x2)1/2]Equation 38
Integrals.
int cosh x dx = sinh x + CEquation 39
int sinh x dx = cosh x + CEquation 40
int sech2 x dx = tanh x + CEquation 41
int csch2 x dx = -coth x + CEquation 42
int sech x tanh x dx = -sech x + CEquation 43
int csch x coth x dx = -csch x + CEquation 44
int dx/(x2 + 1)1/2 = arcsinh x + CEquation 45
int dx/(x2 – 1)1/2 = arccosh x + CEquation 46
int dx/(1 – x2) = arctanh x + CEquation 47
int dx/(1 – x2) = arccoth x + CEquation 48
int dx/[x (1 – x2)1/2] = -arcsech x + CEquation 49
int dx/[|x| (1 + x2)1/2] = -arccsch x + CEquation 50