Mister Exam
Least common denominator pi*sin(pi/(z+1))/(z+1)^2
The solution
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/ pi \
pi*sin|-----|
\z + 1/
-------------
2
(z + 1)
$$\frac{\pi \sin{\left(\frac{\pi}{z + 1} \right)}}{\left(z + 1\right)^{2}}$$
(pi*sin(pi/(z + 1)))/(z + 1)^2
Numerical answer
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3.14159265358979*sin(pi/(z + 1))/(1.0 + z)^2
3.14159265358979*sin(pi/(z + 1))/(1.0 + z)^2
Common denominator
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/ pi \
pi*sin|-----|
\1 + z/
-------------
2
1 + z + 2*z
$$\frac{\pi \sin{\left(\frac{\pi}{z + 1} \right)}}{z^{2} + 2 z + 1}$$
pi*sin(pi/(1 + z))/(1 + z^2 + 2*z)
Powers
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/ -pi*I pi*I\
| ------ -----|
| 1 + z 1 + z|
-pi*I*\- e + e /
---------------------------
2
2*(1 + z)
$$- \frac{i \pi \left(e^{\frac{i \pi}{z + 1}} - e^{- \frac{i \pi}{z + 1}}\right)}{2 \left(z + 1\right)^{2}}$$
-pi*i*(-exp(-pi*i/(1 + z)) + exp(pi*i/(1 + z)))/(2*(1 + z)^2)
Trigonometric part
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/ pi pi \
pi*cos|- -- + -----|
\ 2 1 + z/
--------------------
2
(1 + z)
$$\frac{\pi \cos{\left(- \frac{\pi}{2} + \frac{\pi}{z + 1} \right)}}{\left(z + 1\right)^{2}}$$
pi
--------------------------
2 / pi pi \
(1 + z) *sec|- -- + -----|
\ 2 1 + z/
$$\frac{\pi}{\left(z + 1\right)^{2} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{z + 1} \right)}}$$
/ pi \
2*pi*tan|---------|
\2*(1 + z)/
------------------------------
2 / 2/ pi \\
(1 + z) *|1 + tan |---------||
\ \2*(1 + z)//
$$\frac{2 \pi \tan{\left(\frac{\pi}{2 \left(z + 1\right)} \right)}}{\left(z + 1\right)^{2} \left(\tan^{2}{\left(\frac{\pi}{2 \left(z + 1\right)} \right)} + 1\right)}$$
pi
-------------------
2 / pi \
(1 + z) *csc|-----|
\1 + z/
$$\frac{\pi}{\left(z + 1\right)^{2} \csc{\left(\frac{\pi}{z + 1} \right)}}$$
/ pi \
2*pi*cot|---------|
\2*(1 + z)/
------------------------------
2 / 2/ pi \\
(1 + z) *|1 + cot |---------||
\ \2*(1 + z)//
$$\frac{2 \pi \cot{\left(\frac{\pi}{2 \left(z + 1\right)} \right)}}{\left(z + 1\right)^{2} \left(\cot^{2}{\left(\frac{\pi}{2 \left(z + 1\right)} \right)} + 1\right)}$$
2*pi*cot(pi/(2*(1 + z)))/((1 + z)^2*(1 + cot(pi/(2*(1 + z)))^2))