3
sin (x)
2*sin(x) + -------
2
cos (x)
-------------------
_____________
/ 4
/ sin (x)
/ 1 - -------
/ 2
\/ cos (x)
$$\frac{\frac{\sin^{3}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2 \sin{\left(x \right)}}{\sqrt{- \frac{\sin^{4}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1}}$$
2
/ 2 \
| sin (x)| 4
|2 + -------| *sin (x)
4 2 | 2 |
2*sin (x) 3*sin (x) \ cos (x)/
2*cos(x) + --------- + --------- + ----------------------
3 cos(x) / 4 \
cos (x) | sin (x)|
|1 - -------|*cos(x)
| 2 |
\ cos (x)/
---------------------------------------------------------
_____________
/ 4
/ sin (x)
/ 1 - -------
/ 2
\/ cos (x)
$$\frac{\frac{\left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2\right)^{2} \sin^{4}{\left(x \right)}}{\left(- \frac{\sin^{4}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1\right) \cos{\left(x \right)}} + \frac{2 \sin^{4}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{3 \sin^{2}{\left(x \right)}}{\cos{\left(x \right)}} + 2 \cos{\left(x \right)}}{\sqrt{- \frac{\sin^{4}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1}}$$
/ 3 \
| / 2 \ / 4 2 \ / 2 \ / 2 \ / 4 2 \|
| 2 | sin (x)| | 3*sin (x) 7*sin (x)| | sin (x)| 6 2 | sin (x)| | 2*sin (x) 3*sin (x)||
| sin (x)*|2 + -------|*|6 + --------- + ---------| 3*|2 + -------| *sin (x) 2*sin (x)*|2 + -------|*|2*cos(x) + --------- + ---------||
| 4 2 | 2 | | 4 2 | | 2 | | 2 | | 3 cos(x) ||
| 6*sin (x) 11*sin (x) \ cos (x)/ \ cos (x) cos (x) / \ cos (x)/ \ cos (x)/ \ cos (x) /|
|4 + --------- + ---------- + ------------------------------------------------- + ------------------------ + ----------------------------------------------------------|*sin(x)
| 4 2 4 2 / 4 \ |
| cos (x) cos (x) sin (x) / 4 \ | sin (x)| |
| 1 - ------- | sin (x)| 2 |1 - -------|*cos(x) |
| 2 |1 - -------| *cos (x) | 2 | |
| cos (x) | 2 | \ cos (x)/ |
\ \ cos (x)/ /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_____________
/ 4
/ sin (x)
/ 1 - -------
/ 2
\/ cos (x)
$$\frac{\left(\frac{3 \left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2\right)^{3} \sin^{6}{\left(x \right)}}{\left(- \frac{\sin^{4}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1\right)^{2} \cos^{2}{\left(x \right)}} + \frac{\left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2\right) \left(\frac{3 \sin^{4}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{7 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 6\right) \sin^{2}{\left(x \right)}}{- \frac{\sin^{4}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1} + \frac{2 \left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2\right) \left(\frac{2 \sin^{4}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{3 \sin^{2}{\left(x \right)}}{\cos{\left(x \right)}} + 2 \cos{\left(x \right)}\right) \sin^{2}{\left(x \right)}}{\left(- \frac{\sin^{4}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1\right) \cos{\left(x \right)}} + \frac{6 \sin^{4}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{11 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 4\right) \sin{\left(x \right)}}{\sqrt{- \frac{\sin^{4}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1}}$$