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# Hyperbolic Trigonometry

The hyperbolic Trigonometry includes different hyperbolic Functions. The Trigonometric Functions expressed in the form of ex are known as hyperbolic trigonometric functions.
Now we will see the different Hyperbolic Functions:
Hyperbolic of sine of ‘s’ = sin hs =
Hyperbolic of cosine of ‘s’ = cos h s =
Hyperbolic of Tangent of ‘s’ = tan h s =

Hyperbolic of cotangent of ‘s’ = cot h s =

Hyperbolic of tangent of ‘s’ = tan h s =

Hyperbolic of secant of ‘s’ = sec h s =

Hyperbolic of cosecant of ‘s’ = csc h s =
Now we will talk about the negative hyperbolic function which is given below:
Sin h (-s) = -sin h s,
Cos h (-s) = cos h s,
Tan h (-s) = -tan h s,
Cosec h (-s) = -cosec h s,
Sec h (-s) = sec h s,
Cot h (-s) = -cot h s,
Now we will see the relationship among the hyperbolic functions:
Tan h s = sin h s / cos h s;
Cot h s = 1 / tan h s = cos h s / sin h s;
Sec h s = 1 / cos h s;
Cosec h s = 1 / sin h s;
Cosh2 s – sinh2 s = 1;
Sech2 s + tanh2 s = 1;
Coth2 s - cosech2 s = 1;
Sin h (s + t) = sin h s cos h t + cos h s sin h t;
Cos h (s + t) = cos h s cos h t + sin h s sin h t;
Sin h (s + t) = (tan h s + tan h t) / (1 + (tan h s tan h t) ;
Cot h (s + t) = (cot h s cot h t + 1) / (cot h s + tan h t);
These all are hyperbolic functions, using these functions we can solve any equation which contains hyperbolic value.

## Hyperbolic Functions

In mathematics, hyperbolic Functions are similar to the trigonometric Functions,  and they are defined in terms of the Exponential Function. Here we are going to define three main hyperbolic functions. We also talk about some hyperbolic functions identities involving these functions, with their inverse functions and reciprocal functions.