Hyperbolic Functions

Question 1

What are the identities of sinhx and coshx?

Answer 1

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

Question 2

What is Osborne’s rule

Answer 2

With hyperbolic trig identities, whereever there is a (sinhx)^2 put a minus sign infront of normal trig identities.

Question 3

What do sinhx and coshx differentiate and integrate to

Answer 3

Dy/dx: Sinhx- coshx - sinx - coshx
Integrate the same

Question 4

What is the identity for arsinhx and arcoshx

Answer 4

Arsinhx- ln(x + root x^2 + 1)
Arcoshx- +- ln( x + root x^2 + 1)