Hyperbolic Trigonometry

The hyperbolic Trigonometry includes different hyperbolic Functions. The Trigonometric Functions expressed in the form of e^x 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;
Now we will talk about the addition of hyperbolic functions;
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.