Question

Prove that $\frac{cosh\ x}{1\ -\ tanh\ x} + \frac{sinh\ x}{1\ -\ coth\ x} = sinh\ x + cosh\ x, \ for \ x\ \neq\ 0$.

Answer 1

Hi,

The functions given in this question are Hyperbolic Trigonometric Functions.

I have used the Identities of these Hyperbolic Functions to solve this question.

Other methods include simple mathematical operations like addition, subtraction and LCM etc.

The solution is easy to understand.

Kindly see the Attachment for the detailed answer.

I hope it will help You.