The addition formulas for hyperbolic sine, hyperbolic cosine, and hyperbolic tangent will be achieved via brute .

The Addition Formulas for Hyperbolic Functions are also known as the compound angle formulas (for hyperbolic functions). However, it is the view of $\mathsf{Pr} \infty \mathsf{fWiki}$ that the arguments of the hyperbolic functions are in general not actually angles as they frequently are for the Compound Angle Formulas , and hence is a misnomer.

Hyperbolic functions are used to express the angle of parallelism in hyperbolic geometry. They are used to express Lorentz boosts as hyperbolic rotations in special relativity . They also occur in the solutions of many linear differential equations (such as the equation defining a catenary ), cubic equations , and Laplace's equation in ...

Hyperbolic Functions Formulas. The basic hyperbolic functions formulas along with its graph functions are given below: Hyperbolic Sine Function. The hyperbolic sine function is a function f: R → R is defined by f(x) = [e x – e-x]/2 and it is denoted by sinh x. Sinh x = [e x – e-x]/2 . Graph : y = Sinh x. Hyperbolic Cosine Function

Hyperbolic Angle Sum Formula Find sinh(x + y) and cosh(x + y) in terms of sinh x, cosh x, sinh y and cosh y. Solution sinh(x + y) Recall that: e u− −e−u e + e u sinh(u) = and cosh(u) = . 2 2 The easiest way to approach this problem might be to guess that the hyper­