Simplificación general
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/ ______________ _______________ \
| / ___ / ___ |
\\/ 10 - 2*\/ 5 + \/ 50 - 10*\/ 5 + 8*sin(2*a)/*tan(a)
------------------------------------------------------------
/ pi \
16*tan|-----|
\2 + a/
$$\frac{\left(8 \sin{\left(2 a \right)} + \sqrt{10 - 2 \sqrt{5}} + \sqrt{50 - 10 \sqrt{5}}\right) \tan{\left(a \right)}}{16 \tan{\left(\frac{\pi}{a + 2} \right)}}$$
(sqrt(10 - 2*sqrt(5)) + sqrt(50 - 10*sqrt(5)) + 8*sin(2*a))*tan(a)/(16*tan(pi/(2 + a)))
Unión de expresiones racionales
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/ pi \ /pi + 5*a\ /3*pi + 10*a\
cot|-----|*sin|--------|*sin|-----------|
\2 + a/ \ 5 / \ 10 /
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cot(a)
$$\frac{\sin{\left(\frac{5 a + \pi}{5} \right)} \sin{\left(\frac{10 a + 3 \pi}{10} \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{\cot{\left(a \right)}}$$
cot(pi/(2 + a))*sin((pi + 5*a)/5)*sin((3*pi + 10*a)/10)/cot(a)
Denominador racional
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/ pi \ / 3*pi\ / pi\
cot|-----|*sin|a + ----|*sin|a + --|
\2 + a/ \ 10 / \ 5 /
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cot(a)
$$\frac{\sin{\left(a + \frac{3 \pi}{10} \right)} \sin{\left(a + \frac{\pi}{5} \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{\cot{\left(a \right)}}$$
cot(pi/(2 + a))*sin(a + 3*pi/10)*sin(a + pi/5)/cot(a)
/ pi \ / pi\ / 3*pi\
cot|-----|*sin|a + --|*sin|a + ----|
\2 + a/ \ 5 / \ 10 /
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cot(a)
$$\frac{\sin{\left(a + \frac{\pi}{5} \right)} \sin{\left(a + \frac{3 \pi}{10} \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{\cot{\left(a \right)}}$$
/ / 3*pi\ / 3*pi\\ / / pi\ / pi\\
| I*|-a - ----| I*|a + ----|| | I*|-a - --| I*|a + --||
| \ 10 / \ 10 /| | \ 5 / \ 5 /| / pi \
-\- e + e /*\- e + e /*cot|-----|
\2 + a/
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4*cot(a)
$$- \frac{\left(- e^{i \left(- a - \frac{3 \pi}{10}\right)} + e^{i \left(a + \frac{3 \pi}{10}\right)}\right) \left(- e^{i \left(- a - \frac{\pi}{5}\right)} + e^{i \left(a + \frac{\pi}{5}\right)}\right) \cot{\left(\frac{\pi}{a + 2} \right)}}{4 \cot{\left(a \right)}}$$
-(-exp(i*(-a - 3*pi/10)) + exp(i*(a + 3*pi/10)))*(-exp(i*(-a - pi/5)) + exp(i*(a + pi/5)))*cot(pi/(2 + a))/(4*cot(a))
/ pi \ / pi\ / 3*pi\
cot|-----|*sin|a + --|*sin|a + ----|
\2 + a/ \ 5 / \ 10 /
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cot(a)
$$\frac{\sin{\left(a + \frac{\pi}{5} \right)} \sin{\left(a + \frac{3 \pi}{10} \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{\cot{\left(a \right)}}$$
cot(pi/(2 + a))*sin(a + pi/5)*sin(a + 3*pi/10)/cot(a)
/ pi \ / pi\ / 3*pi\
cot|-----|*sin|a + --|*sin|a + ----|
\2 + a/ \ 5 / \ 10 /
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cot(a)
$$\frac{\sin{\left(a + \frac{\pi}{5} \right)} \sin{\left(a + \frac{3 \pi}{10} \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{\cot{\left(a \right)}}$$
cot(pi/(2 + a))*sin(a + pi/5)*sin(a + 3*pi/10)/cot(a)
Abrimos la expresión
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___________ ___________ ___________ ___________
/ ___ / ___ / ___ / ___
/ pi \ / 5 \/ 5 2 / pi \ / 5 \/ 5 2 / pi \ ___ / 5 \/ 5 2 / pi \ ___ / 5 \/ 5 2 / pi \
cos(a)*cot|-----|*sin(a) / - - ----- *cos (a)*cot|-----| / - - ----- *sin (a)*cot|-----| \/ 5 * / - - ----- *cos (a)*cot|-----| \/ 5 * / - - ----- *sin (a)*cot|-----|
\2 + a/ \/ 8 8 \2 + a/ \/ 8 8 \2 + a/ \/ 8 8 \2 + a/ \/ 8 8 \2 + a/
------------------------ + ----------------------------------- + ----------------------------------- + ----------------------------------------- + -----------------------------------------
cot(a) 4*cot(a) 4*cot(a) 4*cot(a) 4*cot(a)
$$\frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sin^{2}{\left(a \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{4 \cot{\left(a \right)}} + \frac{\sqrt{5} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sin^{2}{\left(a \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{4 \cot{\left(a \right)}} + \frac{\sin{\left(a \right)} \cos{\left(a \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{\cot{\left(a \right)}} + \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \cos^{2}{\left(a \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{4 \cot{\left(a \right)}} + \frac{\sqrt{5} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \cos^{2}{\left(a \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{4 \cot{\left(a \right)}}$$
cos(a)*cot(pi/(2 + a))*sin(a)/cot(a) + sqrt(5/8 - sqrt(5)/8)*cos(a)^2*cot(pi/(2 + a))/(4*cot(a)) + sqrt(5/8 - sqrt(5)/8)*sin(a)^2*cot(pi/(2 + a))/(4*cot(a)) + sqrt(5)*sqrt(5/8 - sqrt(5)/8)*cos(a)^2*cot(pi/(2 + a))/(4*cot(a)) + sqrt(5)*sqrt(5/8 - sqrt(5)/8)*sin(a)^2*cot(pi/(2 + a))/(4*cot(a))
cot(pi/(2 + a))*sin(a + pi/5)*sin(a + (3*pi)/10)/cot(a)
cot(pi/(2 + a))*sin(a + pi/5)*sin(a + (3*pi)/10)/cot(a)
Compilar la expresión
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/ pi \ / pi\ / 3*pi\
cot|-----|*sin|a + --|*sin|a + ----|
\2 + a/ \ 5 / \ 10 /
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cot(a)
$$\frac{\sin{\left(a + \frac{3 \pi}{10} \right)} \sin{\left(a + \frac{\pi}{5} \right)} \cot{\left(\frac{\pi}{a + 2} \right)}}{\cot{\left(a \right)}}$$
cot(pi/(2 + a))*sin(a + pi/5)*sin(a + (3*pi)/10)/cot(a)