2/pi*a\
-1 + cot |----|
\4*b /
---------------
2/pi*a\
1 + cot |----|
\4*b /
$$\frac{\cot^{2}{\left(\frac{\pi a}{4 b} \right)} - 1}{\cot^{2}{\left(\frac{\pi a}{4 b} \right)} + 1}$$
2
------------------------------------
/ 1 \ /pi pi*a\
|1 + ---------------|*cot|-- + ----|
| 2/pi pi*a\| \4 4*b /
| cot |-- + ----||
\ \4 4*b //
$$\frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}\right) \cot{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}$$
/pi pi*a\
2*csc|-- - ----|
\4 4*b /
------------------------------------
/ 2/pi pi*a\\
| csc |-- - ----||
| \4 4*b /| /pi pi*a\
|1 + ---------------|*csc|-- + ----|
| 2/pi pi*a\| \4 4*b /
| csc |-- + ----||
\ \4 4*b //
$$\frac{2 \csc{\left(- \frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}{\left(\frac{\csc^{2}{\left(- \frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}} + 1\right) \csc{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}$$
/pi pi*a\
2*sec|-- + ----|
\4 4*b /
----------------------------------------
/ 2/pi pi*a\ \
| sec |-- + ----| |
| \4 4*b / | / pi pi*a\
|1 + -----------------|*sec|- -- + ----|
| 2/ pi pi*a\| \ 4 4*b /
| sec |- -- + ----||
\ \ 4 4*b //
$$\frac{2 \sec{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{\pi a}{4 b} - \frac{\pi}{4} \right)}}\right) \sec{\left(\frac{\pi a}{4 b} - \frac{\pi}{4} \right)}}$$
/ /pi*a\\ / /pi*a\\
|1 - sin|----||*|1 + tan|----||
\ \2*b // \ \4*b //
-------------------------------
/pi*a\
1 - tan|----|
\4*b /
$$\frac{\left(1 - \sin{\left(\frac{\pi a}{2 b} \right)}\right) \left(\tan{\left(\frac{\pi a}{4 b} \right)} + 1\right)}{1 - \tan{\left(\frac{\pi a}{4 b} \right)}}$$
/pi*a\
2*tan|----|
\4*b /
1 + --------------
2/pi*a\
1 + tan |----|
\4*b /
------------------
/pi pi*a\
tan|-- + ----|
\4 4*b /
$$\frac{1 + \frac{2 \tan{\left(\frac{\pi a}{4 b} \right)}}{\tan^{2}{\left(\frac{\pi a}{4 b} \right)} + 1}}{\tan{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}$$
1
--------------
/pi pi*a\
csc|-- - ----|
\2 2*b /
$$\frac{1}{\csc{\left(- \frac{\pi a}{2 b} + \frac{\pi}{2} \right)}}$$
/ 1 \ /pi pi*a\
|1 + ---------|*csc|-- + ----|
| /pi*a\| \4 4*b /
| csc|----||
\ \2*b //
------------------------------
/pi pi*a\
csc|-- - ----|
\4 4*b /
$$\frac{\left(1 + \frac{1}{\csc{\left(\frac{\pi a}{2 b} \right)}}\right) \csc{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}{\csc{\left(- \frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}$$
/ pi pi*a\
2*cos|- -- + ----|
\ 4 4*b /
--------------------------------------
/ 2/ pi pi*a\\
| cos |- -- + ----||
| \ 4 4*b /| /pi pi*a\
|1 + -----------------|*cos|-- + ----|
| 2/pi pi*a\ | \4 4*b /
| cos |-- + ----| |
\ \4 4*b / /
$$\frac{2 \cos{\left(\frac{\pi a}{4 b} - \frac{\pi}{4} \right)}}{\left(\frac{\cos^{2}{\left(\frac{\pi a}{4 b} - \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}} + 1\right) \cos{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}$$
/ /pi*a\ \
| 2*cot|----| |
| \4*b / | /pi pi*a\
|1 + --------------|*cot|-- + ----|
| 2/pi*a\| \4 4*b /
| 1 + cot |----||
\ \4*b //
$$\left(1 + \frac{2 \cot{\left(\frac{\pi a}{4 b} \right)}}{\cot^{2}{\left(\frac{\pi a}{4 b} \right)} + 1}\right) \cot{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}$$
/ / pi pi*a\\ /pi pi*a\
|1 + cos|- -- + ----||*cos|-- + ----|
\ \ 2 2*b // \4 4*b /
-------------------------------------
/ pi pi*a\
cos|- -- + ----|
\ 4 4*b /
$$\frac{\left(\cos{\left(\frac{\pi a}{2 b} - \frac{\pi}{2} \right)} + 1\right) \cos{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}{\cos{\left(\frac{\pi a}{4 b} - \frac{\pi}{4} \right)}}$$
1
-----------
/-pi*a \
sec|------|
\ 2*b /
$$\frac{1}{\sec{\left(- \frac{\pi a}{2 b} \right)}}$$
/ /pi*a\\ / /pi*a\\
|1 - tan|----||*|1 + sin|----||
\ \4*b // \ \2*b //
-------------------------------
/pi*a\
1 + tan|----|
\4*b /
$$\frac{\left(1 - \tan{\left(\frac{\pi a}{4 b} \right)}\right) \left(\sin{\left(\frac{\pi a}{2 b} \right)} + 1\right)}{\tan{\left(\frac{\pi a}{4 b} \right)} + 1}$$
/ /pi*a\\ /pi pi*a\
|1 + sin|----||*cot|-- + ----|
\ \2*b // \4 4*b /
$$\left(\sin{\left(\frac{\pi a}{2 b} \right)} + 1\right) \cot{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}$$
/pi*a\
1 + sin|----|
\2*b /
--------------
/pi pi*a\
tan|-- + ----|
\4 4*b /
$$\frac{\sin{\left(\frac{\pi a}{2 b} \right)} + 1}{\tan{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}$$
/ /pi*a\\
2*|1 + sin|----||
\ \2*b //
------------------------------------
/ 4/ /1 a \\\
| 8*sin |pi*|- + ---|||
| \ \4 4*b//| /pi*a\
|1 + --------------------|*cos|----|
| /pi*a\ | \2*b /
| 1 + cos|----| |
\ \ b / /
$$\frac{2 \left(\sin{\left(\frac{\pi a}{2 b} \right)} + 1\right)}{\left(1 + \frac{8 \sin^{4}{\left(\pi \left(\frac{a}{4 b} + \frac{1}{4}\right) \right)}}{\cos{\left(\frac{\pi a}{b} \right)} + 1}\right) \cos{\left(\frac{\pi a}{2 b} \right)}}$$
/pi pi*a\
sin|-- + ----|
\2 2*b /
$$\sin{\left(\frac{\pi a}{2 b} + \frac{\pi}{2} \right)}$$
/pi pi*a\
2*tan|-- + ----|
\4 4*b /
-------------------
2/pi pi*a\
1 + tan |-- + ----|
\4 4*b /
$$\frac{2 \tan{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)} + 1}$$
/ 1 \ / pi pi*a\
|1 + ----------------|*sec|- -- + ----|
| / pi pi*a\| \ 4 4*b /
| sec|- -- + ----||
\ \ 2 2*b //
---------------------------------------
/pi pi*a\
sec|-- + ----|
\4 4*b /
$$\frac{\left(1 + \frac{1}{\sec{\left(\frac{\pi a}{2 b} - \frac{\pi}{2} \right)}}\right) \sec{\left(\frac{\pi a}{4 b} - \frac{\pi}{4} \right)}}{\sec{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}$$
2
------------------------------------
/ 1 \ /pi pi*a\
|1 + ---------------|*tan|-- + ----|
| 2/pi pi*a\| \4 4*b /
| tan |-- + ----||
\ \4 4*b //
$$\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}\right) \tan{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}$$
$$\cos{\left(\frac{\pi a}{2 b} \right)}$$
/ /pi*a\\ /pi*a\
|1 + sin|----||*cos|----|
\ \2*b // \2*b /
-------------------------
2/pi pi*a\
2*sin |-- + ----|
\4 4*b /
$$\frac{\left(\sin{\left(\frac{\pi a}{2 b} \right)} + 1\right) \cos{\left(\frac{\pi a}{2 b} \right)}}{2 \sin^{2}{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}$$
2/pi*a\
1 - tan |----|
\4*b /
--------------
2/pi*a\
1 + tan |----|
\4*b /
$$\frac{1 - \tan^{2}{\left(\frac{\pi a}{4 b} \right)}}{\tan^{2}{\left(\frac{\pi a}{4 b} \right)} + 1}$$
1
---------
/pi*a\
sec|----|
\2*b /
$$\frac{1}{\sec{\left(\frac{\pi a}{2 b} \right)}}$$
/pi pi*a\
2*cot|-- + ----|
\4 4*b /
-------------------
2/pi pi*a\
1 + cot |-- + ----|
\4 4*b /
$$\frac{2 \cot{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)} + 1}$$
2/pi pi*a\
4*sin |-- + ----|
\4 4*b /
---------------------------------
/ 4/pi pi*a\\
| 4*sin |-- + ----||
| \4 4*b /| /pi*a\
|1 + -----------------|*cos|----|
| 2/pi*a\ | \2*b /
| cos |----| |
\ \2*b / /
$$\frac{4 \sin^{2}{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{\pi a}{4 b} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{\pi a}{2 b} \right)}} + 1\right) \cos{\left(\frac{\pi a}{2 b} \right)}}$$
/-pi*a \
cos|------|
\ 2*b /
$$\cos{\left(- \frac{\pi a}{2 b} \right)}$$