Hyperbolic Functions Identities

Question 1

sinhx

Answer 1

(e^x - e^-x) / 2

Question 2

coshx

Answer 2

(e^x + e^-x) / 2

Question 3

tanhx

Answer 3

sinhx/coshx

Question 4

cschx

Answer 4

1/sinhx

Question 5

sechx

Answer 5

1/coshx

Question 6

cothx

Answer 6

coshx/sinhx

Question 7

pythagorean identities

Answer 7

cosh²x - sinh²x = 1
sech²x + tanh²x = 1
coth²x - csch²x = 1

Question 8

Sum and Difference Identities of Hyperbolic Sine

Answer 8

sinh(a+b) = sinh a cosh b + cosh a sinh b
sinh(a-b) = sinh a cosh b - cosh a sinh b

Question 9

Sum and Difference Identities of Hyperbolic Cosine

Answer 9

cosh(a+b) = cosh a cosh b + sinh a sinh b
cosh(a-b) = cosh a cosh b - sinh a sinh b

Question 10

Sum and Difference Identities of Hyperbolic Tangent

Answer 10

tan(a+b) = (tanh a + tanh b) / (1 + tanh a tanh b)
tan(a-b) = (tanh a - tanh b) / (1 - tanh a tanh b)

Question 11

Sum and Difference Identities of Hyperbolic Cotangent

Answer 11

coth(a+b) = (coth a coth b + 1) / (coth y + coth x)
coth(a-b) = (coth a coth b - 1) / (coth y - coth x)

Question 12

sinh 2x

Answer 12

2sinh x cosh x

Question 13

sinh² x

Answer 13

1/4 (e^2x - 2 + e^-2x)

Question 14

cosh² x

Answer 14

1/4 (e^2x + 2 + e^-2x)