sec(x)*tan(x)
---------------------------
2 2
coth (sec(x))*sinh (sec(x))
$$\frac{\tan{\left(x \right)} \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth^{2}{\left(\sec{\left(x \right)} \right)}}$$
/ 2 2 \
| 2 2*tan (x)*cosh(sec(x))*sec(x) 2*tan (x)*sec(x) |
|1 + 2*tan (x) - ----------------------------- + --------------------------|*sec(x)
| sinh(sec(x)) 2 |
\ coth(sec(x))*sinh (sec(x))/
-----------------------------------------------------------------------------------
2 2
coth (sec(x))*sinh (sec(x))
$$\frac{\left(2 \tan^{2}{\left(x \right)} - \frac{2 \tan^{2}{\left(x \right)} \cosh{\left(\sec{\left(x \right)} \right)} \sec{\left(x \right)}}{\sinh{\left(\sec{\left(x \right)} \right)}} + \frac{2 \tan^{2}{\left(x \right)} \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth{\left(\sec{\left(x \right)} \right)}} + 1\right) \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth^{2}{\left(\sec{\left(x \right)} \right)}}$$
/ 2 / 2 \ 2 2 2 2 / 2 \ 2 2 2 2 \
| 2 2 2 6*tan (x)*cosh(sec(x))*sec(x) 6*\1 + tan (x)/*cosh(sec(x))*sec(x) 6*cosh (sec(x))*sec (x)*tan (x) 6*tan (x)*sec(x) 6*\1 + tan (x)/*sec(x) 6*sec (x)*tan (x) 12*sec (x)*tan (x)*cosh(sec(x))|
|5 + 6*tan (x) - 2*sec (x)*tan (x) - ----------------------------- - ----------------------------------- + ------------------------------- + -------------------------- + -------------------------- + --------------------------- - -------------------------------|*sec(x)*tan(x)
| sinh(sec(x)) sinh(sec(x)) 2 2 2 2 4 3 |
\ sinh (sec(x)) coth(sec(x))*sinh (sec(x)) coth(sec(x))*sinh (sec(x)) coth (sec(x))*sinh (sec(x)) coth(sec(x))*sinh (sec(x)) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
coth (sec(x))*sinh (sec(x))
$$\frac{\left(- \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \cosh{\left(\sec{\left(x \right)} \right)} \sec{\left(x \right)}}{\sinh{\left(\sec{\left(x \right)} \right)}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth{\left(\sec{\left(x \right)} \right)}} - 2 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)} + 6 \tan^{2}{\left(x \right)} - \frac{6 \tan^{2}{\left(x \right)} \cosh{\left(\sec{\left(x \right)} \right)} \sec{\left(x \right)}}{\sinh{\left(\sec{\left(x \right)} \right)}} + \frac{6 \tan^{2}{\left(x \right)} \cosh^{2}{\left(\sec{\left(x \right)} \right)} \sec^{2}{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)}} + \frac{6 \tan^{2}{\left(x \right)} \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth{\left(\sec{\left(x \right)} \right)}} - \frac{12 \tan^{2}{\left(x \right)} \cosh{\left(\sec{\left(x \right)} \right)} \sec^{2}{\left(x \right)}}{\sinh^{3}{\left(\sec{\left(x \right)} \right)} \coth{\left(\sec{\left(x \right)} \right)}} + \frac{6 \tan^{2}{\left(x \right)} \sec^{2}{\left(x \right)}}{\sinh^{4}{\left(\sec{\left(x \right)} \right)} \coth^{2}{\left(\sec{\left(x \right)} \right)}} + 5\right) \tan{\left(x \right)} \sec{\left(x \right)}}{\sinh^{2}{\left(\sec{\left(x \right)} \right)} \coth^{2}{\left(\sec{\left(x \right)} \right)}}$$