## Hyperbolic Function

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### Important Formulas:

1. If     is a real number, then the exponential function  is defined by     then   

2. The hyperbolic functions    is defined by  

3. The hyperbolic functions   is defined by  

4. Also,  

5. Also,  

6. 

7.   are odd functions.

8.  are even functions.

9. 

10. 

11. 

12. 

13. 

14. 

15. 

16.  

17. 

18.   for all 

19. for   

20. for  

21. for \csc h^{-1}

22. for \csc h^{-1}

23. 

24. 

25. 

26.