List of top Mathematics Questions on Hyperbolic Functions

Evaluate \[ \log\left(\sinh\theta+\sqrt{\sinh^2\theta+1}\right). \]

If \[ \tanh x=\frac13, \] then \[ 6\sinh^4x+2\cosh^4x+2\sinh^2x+\cosh^2x= \]

If \(\sinh x=\frac{12}{5}\), then \[ \cosh2x-\sinh2x= \]

If \( a \) is a real number and \( 2\sinh^2 x - 3\cosh x + a = 0 \) has a solution, then the range of \( a \) is:

\(\text{Cosech}^{-1}2+\text{Cosech}^{-1}\left(-\dfrac12\right)=\)

If \[ \tanh^{-1}(x)=\log\sqrt3 \] and \[ \cosh^{-1}(y)=\log(1+\sqrt2), \] then \[ \operatorname{sech}^{-1}(xy)= \]

Evaluate \[ e^{Sinh^{-1}(2\sqrt2)}+e^{Cosh^{-1}(3)} \]

If \( \sinh^{-1}(2) + \sinh^{-1}(3) = \alpha \), then \( \cosh \alpha = \)

If \( u=log_{e}[tan(\frac{\pi}{4}+\frac{\theta}{2})], \) then \( sinh~u= \)

If \[ u=\log\tan\left(\frac{\pi}{4}+\frac{\theta}{2}\right), \] then \[ \tanh\frac{u}{2} = \]

If $\sinh x = \frac{3}{4}$, then $\cosh 2x =$

Consider the following statements
Statement-I: $\cosh^{-1}x = \tanh^{-1}x$ has no solution
Statement-II: $\cosh^{-1}x = \coth^{-1}x$ has only one solution
The correct answer is

$\coth^2 x - \tanh^2 x =$

If $\text{Sinh}^{-1}x = \text{Cosh}^{-1}y = \log(1+\sqrt{2})$ then $\text{Tan}^{-1}(x+y) =$

If one solution of the equation \[ \cosh x - \frac{4}{5} \sinh x = 1 \text{ is } x = 0, \] then the other solution is:

The value of \[ \tanh(\log x) \] is

Let \(\theta\in \mathbb{R}\) such that \[ 3\sinh(2\theta)=13-3e^{2\theta}, \] then \(\theta=\)

For any real number \(n\in \mathbb{R}\), \[ (\cosh x+\sinh x)^n= \]

Let \(x\in \mathbb{R}\) and \(|x|\lt 1\). Then \[ \tanh^{-1}x= \]

If \[ \operatorname{cosech}x=\frac{4}{5}, \] then \[ \cosh x= \] is:

If \[ 2\cosh2x+10\sinh2x=5, \] then \(x=\)

If \[ 4+6(e^{2x}+1)\tanh x = 11\cosh x+11\sinh x, \] then \[ x= \]