Hyperbolic Functions - I

Hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh" and the hyperbolic cosine "cosh" from which are derived the hyperbolic tangent "tanh" and so on, corresponding to the derived trigonometric functions. 

Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the equilateral hyperbola.

The hyperbolic functions cosh x and sinh x are defined using the exponential function e^x. Following are the definitions of cosh x , sinh x and tanh x.

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

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

tanh x = (e^x - e^-x)/(e^x + e^-x)

Hyperbolic sine and cosine satisfy the identity cosh² - sinh²=1
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