dr.trovacek
New member
- Joined
- Apr 3, 2017
- Messages
- 23
Can't prove these, need help.
1.
[MATH]\sinh^2x = \frac {1}{1 + \coth^2 x}[/MATH]
So I took the right side: [MATH] \left ( 1 + \frac{\cosh^2 x}{\sinh^2 x} \right )^{-1} = \frac{\sinh^2 x}{\cosh^2 x + \sinh^2 x}[/MATH]
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.
[MATH] \sinh \frac { x } { 2 } = \operatorname { sgn } ( x ) \cdot \sqrt { \frac { \cosh x - 1 } { 2 } }[/MATH]
Never solved an equation with [MATH] \operatorname { sgn }[/MATH] in it, so I assume that may be the problem. I just squared both sides of the equation and assumed [MATH]\operatorname { sgnx} = \pm 1[/MATH] but it doesn't work .
1.
[MATH]\sinh^2x = \frac {1}{1 + \coth^2 x}[/MATH]
So I took the right side: [MATH] \left ( 1 + \frac{\cosh^2 x}{\sinh^2 x} \right )^{-1} = \frac{\sinh^2 x}{\cosh^2 x + \sinh^2 x}[/MATH]
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.
[MATH] \sinh \frac { x } { 2 } = \operatorname { sgn } ( x ) \cdot \sqrt { \frac { \cosh x - 1 } { 2 } }[/MATH]
Never solved an equation with [MATH] \operatorname { sgn }[/MATH] in it, so I assume that may be the problem. I just squared both sides of the equation and assumed [MATH]\operatorname { sgnx} = \pm 1[/MATH] but it doesn't work .