#### dr.trovacek

##### New member

- Joined
- Apr 3, 2017

- Messages
- 23

1.

\(\displaystyle \sinh^2x = \frac {1}{1 + \coth^2 x}\)

So I took the right side: \(\displaystyle \left ( 1 + \frac{\cosh^2 x}{\sinh^2 x} \right )^{-1} = \frac{\sinh^2 x}{\cosh^2 x + \sinh^2 x}\)

The denominator is not equal to 1, so where did I go wrong?

Tried to check it with mathway.com, but it tells me that expression is not true

2.

\(\displaystyle \sinh \frac { x } { 2 } = \operatorname { sgn } ( x ) \cdot \sqrt { \frac { \cosh x - 1 } { 2 } }\)

Never solved an equation with \(\displaystyle \operatorname { sgn }\) in it, so I assume that may be the problem. I just squared both sides of the equation and assumed \(\displaystyle \operatorname { sgnx} = \pm 1\) but it doesn't work .