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Общий знаменатель 4*(atan(sin(x)/(1+cos(x)) ... (x))+1)/sqrt(3))/sqrt(3))

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Примеры

Решение

Вы ввели [src]
  /                       / 2*sin(x)     \\
  |                       |---------- + 1||
  |                       |1 + cos(x)    ||
  |    /  sin(x)  \   atan|--------------||
  |atan|----------|       |      ___     ||
  |    \1 + cos(x)/       \    \/ 3      /|
4*|---------------- - --------------------|
  |       2                    ___        |
  \                          \/ 3         /
4(−33atan⁡(13(1+2sin⁡(x)cos⁡(x)+1))+12atan⁡(sin⁡(x)cos⁡(x)+1))4 \left(- \frac{\sqrt{3}}{3} \operatorname{atan}{\left (\frac{1}{\sqrt{3}} \left(1 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}\right) \right )} + \frac{1}{2} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}\right)
Степени [src]
                                 /  ___ /     2*sin(x) \\
                                 |\/ 3 *|1 + ----------||
                         ___     |      \    1 + cos(x)/|
                     4*\/ 3 *atan|----------------------|
      /  sin(x)  \               \          3           /
2*atan|----------| - ------------------------------------
      \1 + cos(x)/                    3
−433atan⁡(33(1+2sin⁡(x)cos⁡(x)+1))+2atan⁡(sin⁡(x)cos⁡(x)+1)- \frac{4 \sqrt{3}}{3} \operatorname{atan}{\left (\frac{\sqrt{3}}{3} \left(1 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}\right) \right )} + 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}
                         ___     /  ___ /1      2*sin(x)   \\
                     4*\/ 3 *atan|\/ 3 *|- + --------------||
      /  sin(x)  \               \      \3   3*(1 + cos(x))//
2*atan|----------| - ----------------------------------------
      \1 + cos(x)/                      3
−433atan⁡(3(13+2sin⁡(x)3cos⁡(x)+3))+2atan⁡(sin⁡(x)cos⁡(x)+1)- \frac{4 \sqrt{3}}{3} \operatorname{atan}{\left (\sqrt{3} \left(\frac{1}{3} + \frac{2 \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3}\right) \right )} + 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}
Численный ответ [src]
2.0*atan(sin(x)/(1 + cos(x))) - 2.3094010767585*atan(((2*sin(x))/(1 + cos(x)) + 1)/sqrt(3))
Рациональный знаменатель [src]
                                 /  ___       ___       \
      /  sin(x)  \       ___     |\/ 3    2*\/ 3 *sin(x)|
6*atan|----------| - 4*\/ 3 *atan|----- + --------------|
      \1 + cos(x)/               \  3     3*(1 + cos(x))/
---------------------------------------------------------
                            3
13(6atan⁡(sin⁡(x)cos⁡(x)+1)−43atan⁡(33+23sin⁡(x)3cos⁡(x)+3))\frac{1}{3} \left(6 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - 4 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3}}{3} + \frac{2 \sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}\right)
Объединение рациональных выражений [src]
  /                                 /  ___                        \\
  |      /  sin(x)  \       ___     |\/ 3 *(1 + 2*sin(x) + cos(x))||
2*|3*atan|----------| - 2*\/ 3 *atan|-----------------------------||
  \      \1 + cos(x)/               \        3*(1 + cos(x))       //
--------------------------------------------------------------------
                                 3
13(6atan⁡(sin⁡(x)cos⁡(x)+1)−43atan⁡(3(2sin⁡(x)+cos⁡(x)+1)3cos⁡(x)+3))\frac{1}{3} \left(6 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - 4 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \left(2 \sin{\left (x \right )} + \cos{\left (x \right )} + 1\right)}{3 \cos{\left (x \right )} + 3} \right )}\right)
Общее упрощение [src]
                                 /  ___                        \
                         ___     |\/ 3 *(1 + 2*sin(x) + cos(x))|
                     4*\/ 3 *atan|-----------------------------|
      /  sin(x)  \               \        3*(1 + cos(x))       /
2*atan|----------| - -------------------------------------------
      \1 + cos(x)/                        3
2atan⁡(sin⁡(x)cos⁡(x)+1)−433atan⁡(3(2sin⁡(x)+cos⁡(x)+1)3cos⁡(x)+3)2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - \frac{4 \sqrt{3}}{3} \operatorname{atan}{\left (\frac{\sqrt{3} \left(2 \sin{\left (x \right )} + \cos{\left (x \right )} + 1\right)}{3 \cos{\left (x \right )} + 3} \right )}
Собрать выражение [src]
        / 2*sin(x)     \                     
        |---------- + 1|                     
        |1 + cos(x)    |                     
  4*atan|--------------|         /  sin(x)  \
        |      ___     |   4*atan|----------|
        \    \/ 3      /         \1 + cos(x)/
- ---------------------- + ------------------
            ___                    2         
          \/ 3
−433atan⁡(13(1+2sin⁡(x)cos⁡(x)+1))+42atan⁡(sin⁡(x)cos⁡(x)+1)- 4 \frac{\sqrt{3}}{3} \operatorname{atan}{\left (\frac{1}{\sqrt{3}} \left(1 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}\right) \right )} + \frac{4}{2} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}
                         ___     /         1                    cos(x)                2*sin(x)      \
                     4*\/ 3 *atan|-------------------- + -------------------- + --------------------|
                                 |  ___     ___            ___     ___            ___     ___       |
      /  sin(x)  \               \\/ 3  + \/ 3 *cos(x)   \/ 3  + \/ 3 *cos(x)   \/ 3  + \/ 3 *cos(x)/
2*atan|----------| - --------------------------------------------------------------------------------
      \1 + cos(x)/                                          3
2atan⁡(sin⁡(x)cos⁡(x)+1)−433atan⁡(2sin⁡(x)3cos⁡(x)+3+cos⁡(x)3cos⁡(x)+3+13cos⁡(x)+3)2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - \frac{4 \sqrt{3}}{3} \operatorname{atan}{\left (\frac{2 \sin{\left (x \right )}}{\sqrt{3} \cos{\left (x \right )} + \sqrt{3}} + \frac{\cos{\left (x \right )}}{\sqrt{3} \cos{\left (x \right )} + \sqrt{3}} + \frac{1}{\sqrt{3} \cos{\left (x \right )} + \sqrt{3}} \right )}
Комбинаторика [src]
  /                                 /  ___       ___       \\
  |      /  sin(x)  \       ___     |\/ 3    2*\/ 3 *sin(x)||
2*|3*atan|----------| - 2*\/ 3 *atan|----- + --------------||
  \      \1 + cos(x)/               \  3     3*(1 + cos(x))//
-------------------------------------------------------------
                              3
13(6atan⁡(sin⁡(x)cos⁡(x)+1)−43atan⁡(33+23sin⁡(x)3cos⁡(x)+3))\frac{1}{3} \left(6 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - 4 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3}}{3} + \frac{2 \sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}\right)
Общий знаменатель [src]
                                 /  ___       ___       \
                         ___     |\/ 3    2*\/ 3 *sin(x)|
                     4*\/ 3 *atan|----- + --------------|
      /  sin(x)  \               \  3     3*(1 + cos(x))/
2*atan|----------| - ------------------------------------
      \1 + cos(x)/                    3
2atan⁡(sin⁡(x)cos⁡(x)+1)−433atan⁡(33+23sin⁡(x)3cos⁡(x)+3)2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - \frac{4 \sqrt{3}}{3} \operatorname{atan}{\left (\frac{\sqrt{3}}{3} + \frac{2 \sqrt{3} \sin{\left (x \right )}}{3 \cos{\left (x \right )} + 3} \right )}
Тригонометрическая часть [src]
                                 /  ___ /     2*sin(x) \\
                                 |\/ 3 *|1 + ----------||
                         ___     |      \    1 + cos(x)/|
                     4*\/ 3 *atan|----------------------|
      /  sin(x)  \               \          3           /
2*atan|----------| - ------------------------------------
      \1 + cos(x)/                    3
−433atan⁡(33(1+2sin⁡(x)cos⁡(x)+1))+2atan⁡(sin⁡(x)cos⁡(x)+1)- \frac{4 \sqrt{3}}{3} \operatorname{atan}{\left (\frac{\sqrt{3}}{3} \left(1 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}\right) \right )} + 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}
Раскрыть выражение [src]
                                 /  ___ /     2*sin(x) \\
                                 |\/ 3 *|1 + ----------||
                         ___     |      \    1 + cos(x)/|
                     4*\/ 3 *atan|----------------------|
      /  sin(x)  \               \          3           /
2*atan|----------| - ------------------------------------
      \1 + cos(x)/                    3
−433atan⁡(33(1+2sin⁡(x)cos⁡(x)+1))+2atan⁡(sin⁡(x)cos⁡(x)+1)- \frac{4 \sqrt{3}}{3} \operatorname{atan}{\left (\frac{\sqrt{3}}{3} \left(1 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}\right) \right )} + 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}