Sr Examen
¿Cómo vas a descomponer esta tan(pi/(4+a))+tan(pi/(4-a)) expresión en fracciones?
Solución
Ha introducido
[src]
/ pi \ / pi \ tan|-----| + tan|-----| \4 + a/ \4 - a/
$$\tan{\left(\frac{\pi}{4 - a} \right)} + \tan{\left(\frac{\pi}{a + 4} \right)}$$
tan(pi/(4 + a)) + tan(pi/(4 - a))
Simplificación general
[src]
/ pi \ / pi \
- tan|------| + tan|-----|
\-4 + a/ \4 + a/
$$- \tan{\left(\frac{\pi}{a - 4} \right)} + \tan{\left(\frac{\pi}{a + 4} \right)}$$
-tan(pi/(-4 + a)) + tan(pi/(4 + a))
Potencias
[src]
/ pi*I -pi*I \ / pi*I -pi*I \
| ----- ------| | ----- ------|
| 4 + a 4 + a | | 4 - a 4 - a |
I*\- e + e / I*\- e + e /
---------------------- + ----------------------
pi*I -pi*I pi*I -pi*I
----- ------ ----- ------
4 + a 4 + a 4 - a 4 - a
e + e e + e
$$\frac{i \left(- e^{\frac{i \pi}{4 - a}} + e^{- \frac{i \pi}{4 - a}}\right)}{e^{\frac{i \pi}{4 - a}} + e^{- \frac{i \pi}{4 - a}}} + \frac{i \left(- e^{\frac{i \pi}{a + 4}} + e^{- \frac{i \pi}{a + 4}}\right)}{e^{\frac{i \pi}{a + 4}} + e^{- \frac{i \pi}{a + 4}}}$$
i*(-exp(pi*i/(4 + a)) + exp(-pi*i/(4 + a)))/(exp(pi*i/(4 + a)) + exp(-pi*i/(4 + a))) + i*(-exp(pi*i/(4 - a)) + exp(-pi*i/(4 - a)))/(exp(pi*i/(4 - a)) + exp(-pi*i/(4 - a)))
Parte trigonométrica
[src]
/ pi \ / pi \
- tan|------| + tan|-----|
\-4 + a/ \4 + a/
$$- \tan{\left(\frac{\pi}{a - 4} \right)} + \tan{\left(\frac{\pi}{a + 4} \right)}$$
2/ pi \ 2/ pi \
2*sin |-----| 2*sin |-----|
\4 + a/ \4 - a/
------------- + -------------
/ 2*pi\ / 2*pi\
sin|-----| sin|-----|
\4 + a/ \4 - a/
$$\frac{2 \sin^{2}{\left(\frac{\pi}{4 - a} \right)}}{\sin{\left(\frac{2 \pi}{4 - a} \right)}} + \frac{2 \sin^{2}{\left(\frac{\pi}{a + 4} \right)}}{\sin{\left(\frac{2 \pi}{a + 4} \right)}}$$
/ pi \ / pi \ sec|-----| sec|-----| \4 + a/ \4 - a/ ---------- + ---------- / pi \ / pi \ csc|-----| csc|-----| \4 + a/ \4 - a/
$$\frac{\sec{\left(\frac{\pi}{a + 4} \right)}}{\csc{\left(\frac{\pi}{a + 4} \right)}} + \frac{\sec{\left(\frac{\pi}{4 - a} \right)}}{\csc{\left(\frac{\pi}{4 - a} \right)}}$$
/ pi \ / pi \
sec|-----| sec|------|
\4 + a/ \-4 + a/
----------------- - ------------------
/ pi pi \ / pi pi \
sec|- -- + -----| sec|- -- + ------|
\ 2 4 + a/ \ 2 -4 + a/
$$- \frac{\sec{\left(\frac{\pi}{a - 4} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{a - 4} \right)}} + \frac{\sec{\left(\frac{\pi}{a + 4} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{a + 4} \right)}}$$
/ pi pi \ / pi pi \
cos|- -- + -----| cos|- -- + -----|
\ 2 4 + a/ \ 2 4 - a/
----------------- + -----------------
/ pi \ / pi \
cos|-----| cos|-----|
\4 + a/ \4 - a/
$$\frac{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{a + 4} \right)}}{\cos{\left(\frac{\pi}{a + 4} \right)}} + \frac{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{4 - a} \right)}}{\cos{\left(\frac{\pi}{4 - a} \right)}}$$
/pi pi \ /pi pi \
csc|-- - -----| csc|-- - -----|
\2 4 + a/ \2 4 - a/
--------------- + ---------------
/ pi \ / pi \
csc|-----| csc|-----|
\4 + a/ \4 - a/
$$\frac{\csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 4} \right)}}{\csc{\left(\frac{\pi}{a + 4} \right)}} + \frac{\csc{\left(\frac{\pi}{2} - \frac{\pi}{4 - a} \right)}}{\csc{\left(\frac{\pi}{4 - a} \right)}}$$
2/ pi \ 2/ pi \
2*sin |------| 2*sin |-----|
\-4 + a/ \4 + a/
- -------------- + -------------
/ 2*pi \ / 2*pi\
sin|------| sin|-----|
\-4 + a/ \4 + a/
$$- \frac{2 \sin^{2}{\left(\frac{\pi}{a - 4} \right)}}{\sin{\left(\frac{2 \pi}{a - 4} \right)}} + \frac{2 \sin^{2}{\left(\frac{\pi}{a + 4} \right)}}{\sin{\left(\frac{2 \pi}{a + 4} \right)}}$$
1 1 ---------- - ----------- / pi \ / pi \ cot|-----| cot|------| \4 + a/ \-4 + a/
$$\frac{1}{\cot{\left(\frac{\pi}{a + 4} \right)}} - \frac{1}{\cot{\left(\frac{\pi}{a - 4} \right)}}$$
1 1 ---------- + ---------- / pi \ / pi \ cot|-----| cot|-----| \4 + a/ \4 - a/
$$\frac{1}{\cot{\left(\frac{\pi}{a + 4} \right)}} + \frac{1}{\cot{\left(\frac{\pi}{4 - a} \right)}}$$
/ pi pi \ / pi pi \
cos|- -- + -----| cos|- -- + ------|
\ 2 4 + a/ \ 2 -4 + a/
----------------- - ------------------
/ pi \ / pi \
cos|-----| cos|------|
\4 + a/ \-4 + a/
$$\frac{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{a + 4} \right)}}{\cos{\left(\frac{\pi}{a + 4} \right)}} - \frac{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{a - 4} \right)}}{\cos{\left(\frac{\pi}{a - 4} \right)}}$$
/ pi \ / pi \
sec|-----| sec|-----|
\4 + a/ \4 - a/
----------------- + -----------------
/ pi pi \ / pi pi \
sec|- -- + -----| sec|- -- + -----|
\ 2 4 + a/ \ 2 4 - a/
$$\frac{\sec{\left(\frac{\pi}{4 - a} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{4 - a} \right)}} + \frac{\sec{\left(\frac{\pi}{a + 4} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{a + 4} \right)}}$$
/ pi \ / pi \ sin|-----| sin|-----| \4 + a/ \4 - a/ ---------- + ---------- / pi \ / pi \ cos|-----| cos|-----| \4 + a/ \4 - a/
$$\frac{\sin{\left(\frac{\pi}{4 - a} \right)}}{\cos{\left(\frac{\pi}{4 - a} \right)}} + \frac{\sin{\left(\frac{\pi}{a + 4} \right)}}{\cos{\left(\frac{\pi}{a + 4} \right)}}$$
/pi pi \ /pi pi \
csc|-- - -----| csc|-- - ------|
\2 4 + a/ \2 -4 + a/
--------------- - ----------------
/ pi \ / pi \
csc|-----| csc|------|
\4 + a/ \-4 + a/
$$\frac{\csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 4} \right)}}{\csc{\left(\frac{\pi}{a + 4} \right)}} - \frac{\csc{\left(\frac{\pi}{2} - \frac{\pi}{a - 4} \right)}}{\csc{\left(\frac{\pi}{a - 4} \right)}}$$
csc(pi/2 - pi/(4 + a))/csc(pi/(4 + a)) - csc(pi/2 - pi/(-4 + a))/csc(pi/(-4 + a))