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sin(90+a)*sin(180-a)*(tan ... 180+a)+tan(270-a))еслиa=3 (упростите выражение)

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Примеры

Решение

Вы ввели [src]
sin(90 + a)*sin(180 - a)*(tan(180 + a) + tan(270 - a))
(tan⁡(270−a)+tan⁡(a+180))sin⁡(180−a)sin⁡(a+90)\left(\tan{\left(270 - a \right)} + \tan{\left(a + 180 \right)}\right) \sin{\left(180 - a \right)} \sin{\left(a + 90 \right)}
Подстановка условия [src]
sin(90 + a)*sin(180 - a)*(tan(180 + a) + tan(270 - a)) при a = 3
подставляем
sin(90 + a)*sin(180 - a)*(tan(180 + a) + tan(270 - a))
(tan⁡(270−a)+tan⁡(a+180))sin⁡(180−a)sin⁡(a+90)\left(\tan{\left(270 - a \right)} + \tan{\left(a + 180 \right)}\right) \sin{\left(180 - a \right)} \sin{\left(a + 90 \right)}
(-tan(180 + a) + tan(-270 + a))*sin(-180 + a)*sin(90 + a)
(tan⁡(a−270)−tan⁡(a+180))sin⁡(a−180)sin⁡(a+90)\left(\tan{\left(a - 270 \right)} - \tan{\left(a + 180 \right)}\right) \sin{\left(a - 180 \right)} \sin{\left(a + 90 \right)}
переменные
a = 3
a=3a = 3
(-tan(180 + (3)) + tan(-270 + (3)))*sin(-180 + (3))*sin(90 + (3))
(tan⁡((3)−270)−tan⁡((3)+180))sin⁡((3)−180)sin⁡((3)+90)\left(\tan{\left((3) - 270 \right)} - \tan{\left((3) + 180 \right)}\right) \sin{\left((3) - 180 \right)} \sin{\left((3) + 90 \right)}
(-tan(180 + 3) + tan(-270 + 3))*sin(-180 + 3)*sin(90 + 3)
(−tan⁡(3+180)+tan⁡(−270+3))sin⁡(−180+3)sin⁡(3+90)\left(- \tan{\left(3 + 180 \right)} + \tan{\left(-270 + 3 \right)}\right) \sin{\left(-180 + 3 \right)} \sin{\left(3 + 90 \right)}
-(-tan(183) - tan(267))*sin(93)*sin(177)
−(−tan⁡(183)−tan⁡(267))sin⁡(93)sin⁡(177)- \left(- \tan{\left(183 \right)} - \tan{\left(267 \right)}\right) \sin{\left(93 \right)} \sin{\left(177 \right)}
Степени [src]
-(-tan(-270 + a) + tan(180 + a))*sin(-180 + a)*sin(90 + a)
−(−tan⁡(a−270)+tan⁡(a+180))sin⁡(a−180)sin⁡(a+90)- \left(- \tan{\left(a - 270 \right)} + \tan{\left(a + 180 \right)}\right) \sin{\left(a - 180 \right)} \sin{\left(a + 90 \right)}
                                                                 /  /   I*(270 - a)    I*(-270 + a)\     /   I*(180 + a)    I*(-180 - a)\\ 
 /   I*(-180 + a)    I*(180 - a)\ /   I*(-90 - a)    I*(90 + a)\ |I*\- e            + e            /   I*\- e            + e            /| 
-\- e             + e           /*\- e            + e          /*|---------------------------------- + ----------------------------------| 
                                                                 |    I*(-270 + a)    I*(270 - a)          I*(-180 - a)    I*(180 + a)   | 
                                                                 \   e             + e                    e             + e              / 
-------------------------------------------------------------------------------------------------------------------------------------------
                                                                     4
−(i(−ei(270−a)+ei(a−270))ei(270−a)+ei(a−270)+i(ei(−a−180)−ei(a+180))ei(−a−180)+ei(a+180))(ei(180−a)−ei(a−180))(−ei(−a−90)+ei(a+90))4- \frac{\left(\frac{i \left(- e^{i \left(270 - a\right)} + e^{i \left(a - 270\right)}\right)}{e^{i \left(270 - a\right)} + e^{i \left(a - 270\right)}} + \frac{i \left(e^{i \left(- a - 180\right)} - e^{i \left(a + 180\right)}\right)}{e^{i \left(- a - 180\right)} + e^{i \left(a + 180\right)}}\right) \left(e^{i \left(180 - a\right)} - e^{i \left(a - 180\right)}\right) \left(- e^{i \left(- a - 90\right)} + e^{i \left(a + 90\right)}\right)}{4}
Численный ответ [src]
(tan(180 + a) + tan(270 - a))*sin(90 + a)*sin(180 - a)
Рациональный знаменатель [src]
sin(-180 + a)*sin(90 + a)*tan(-270 + a) - sin(-180 + a)*sin(90 + a)*tan(180 + a)
sin⁡(a−180)sin⁡(a+90)tan⁡(a−270)−sin⁡(a−180)sin⁡(a+90)tan⁡(a+180)\sin{\left(a - 180 \right)} \sin{\left(a + 90 \right)} \tan{\left(a - 270 \right)} - \sin{\left(a - 180 \right)} \sin{\left(a + 90 \right)} \tan{\left(a + 180 \right)}
(-tan(180 + a) + tan(-270 + a))*sin(-180 + a)*sin(90 + a)
(tan⁡(a−270)−tan⁡(a+180))sin⁡(a−180)sin⁡(a+90)\left(\tan{\left(a - 270 \right)} - \tan{\left(a + 180 \right)}\right) \sin{\left(a - 180 \right)} \sin{\left(a + 90 \right)}
Объединение рациональных выражений [src]
-(-tan(-270 + a) + tan(180 + a))*sin(-180 + a)*sin(90 + a)
−(−tan⁡(a−270)+tan⁡(a+180))sin⁡(a−180)sin⁡(a+90)- \left(- \tan{\left(a - 270 \right)} + \tan{\left(a + 180 \right)}\right) \sin{\left(a - 180 \right)} \sin{\left(a + 90 \right)}
Общее упрощение [src]
(-tan(180 + a) + tan(-270 + a))*sin(-180 + a)*sin(90 + a)
(tan⁡(a−270)−tan⁡(a+180))sin⁡(a−180)sin⁡(a+90)\left(\tan{\left(a - 270 \right)} - \tan{\left(a + 180 \right)}\right) \sin{\left(a - 180 \right)} \sin{\left(a + 90 \right)}
Собрать выражение [src]
cos(270)*tan(-270 + a)   cos(-90 + 2*a)*tan(180 + a)   cos(270)*tan(180 + a)   cos(-90 + 2*a)*tan(-270 + a)
---------------------- + --------------------------- - --------------------- - ----------------------------
          2                           2                          2                          2
−12cos⁡(2a−90)tan⁡(a−270)+12cos⁡(2a−90)tan⁡(a+180)+12cos⁡(270)tan⁡(a−270)−12cos⁡(270)tan⁡(a+180)- \frac{1}{2} \cos{\left (2 a - 90 \right )} \tan{\left (a - 270 \right )} + \frac{1}{2} \cos{\left (2 a - 90 \right )} \tan{\left (a + 180 \right )} + \frac{1}{2} \cos{\left (270 \right )} \tan{\left (a - 270 \right )} - \frac{1}{2} \cos{\left (270 \right )} \tan{\left (a + 180 \right )}
(tan(180 + a) + tan(270 - a))*sin(90 + a)*sin(180 - a)
(tan⁡(−a+270)+tan⁡(a+180))sin⁡(−a+180)sin⁡(a+90)\left(\tan{\left (- a + 270 \right )} + \tan{\left (a + 180 \right )}\right) \sin{\left (- a + 180 \right )} \sin{\left (a + 90 \right )}
Общий знаменатель [src]
sin(-180 + a)*sin(90 + a)*tan(-270 + a) - sin(-180 + a)*sin(90 + a)*tan(180 + a)
sin⁡(a−180)sin⁡(a+90)tan⁡(a−270)−sin⁡(a−180)sin⁡(a+90)tan⁡(a+180)\sin{\left(a - 180 \right)} \sin{\left(a + 90 \right)} \tan{\left(a - 270 \right)} - \sin{\left(a - 180 \right)} \sin{\left(a + 90 \right)} \tan{\left(a + 180 \right)}
Тригонометрическая часть [src]
(tan(180 + a) + tan(270 - a))*sin(90 + a)*sin(180 - a)
(tan⁡(−a+270)+tan⁡(a+180))sin⁡(−a+180)sin⁡(a+90)\left(\tan{\left (- a + 270 \right )} + \tan{\left (a + 180 \right )}\right) \sin{\left (- a + 180 \right )} \sin{\left (a + 90 \right )}
Комбинаторика [src]
-(-tan(-270 + a) + tan(180 + a))*sin(-180 + a)*sin(90 + a)
−(−tan⁡(a−270)+tan⁡(a+180))sin⁡(a−180)sin⁡(a+90)- \left(- \tan{\left(a - 270 \right)} + \tan{\left(a + 180 \right)}\right) \sin{\left(a - 180 \right)} \sin{\left(a + 90 \right)}
Раскрыть выражение [src]
   2                                   2                                 2                                   2                                 2                                 2                                   2                                   2                                                                                                                                                                                                                                                                                                                                                                   
cos (a)*sin(90)*sin(180)*tan(270)   sin (a)*cos(90)*cos(180)*tan(a)   cos (a)*sin(90)*sin(180)*tan(180)   cos (a)*sin(90)*sin(180)*tan(a)   cos (a)*sin(90)*sin(180)*tan(a)   sin (a)*cos(90)*cos(180)*tan(270)   sin (a)*cos(90)*cos(180)*tan(180)   sin (a)*cos(90)*cos(180)*tan(a)   cos(90)*cos(a)*sin(180)*sin(a)*tan(270)   cos(180)*cos(a)*sin(90)*sin(a)*tan(a)   cos(90)*cos(a)*sin(180)*sin(a)*tan(180)   cos(90)*cos(a)*sin(180)*sin(a)*tan(a)   cos(90)*cos(a)*sin(180)*sin(a)*tan(a)   cos(180)*cos(a)*sin(90)*sin(a)*tan(270)   cos(180)*cos(a)*sin(90)*sin(a)*tan(180)   cos(180)*cos(a)*sin(90)*sin(a)*tan(a)
--------------------------------- + ------------------------------- + --------------------------------- + ------------------------------- - ------------------------------- - --------------------------------- - --------------------------------- - ------------------------------- + --------------------------------------- + ------------------------------------- + --------------------------------------- + ------------------------------------- - ------------------------------------- - --------------------------------------- - --------------------------------------- - -------------------------------------
       1 + tan(270)*tan(a)                1 + tan(270)*tan(a)                1 - tan(180)*tan(a)                1 - tan(180)*tan(a)               1 + tan(270)*tan(a)                1 + tan(270)*tan(a)                 1 - tan(180)*tan(a)                1 - tan(180)*tan(a)                   1 + tan(270)*tan(a)                      1 + tan(270)*tan(a)                      1 - tan(180)*tan(a)                      1 - tan(180)*tan(a)                     1 + tan(270)*tan(a)                      1 + tan(270)*tan(a)                       1 - tan(180)*tan(a)                      1 - tan(180)*tan(a)
sin⁡2(a)cos⁡(90)cos⁡(180)tan⁡(a)tan⁡(270)tan⁡(a)+1−sin⁡2(a)cos⁡(90)cos⁡(180)tan⁡(270)tan⁡(270)tan⁡(a)+1+sin⁡(90)sin⁡(a)cos⁡(180)cos⁡(a)tan⁡(a)tan⁡(270)tan⁡(a)+1−sin⁡(180)sin⁡(a)cos⁡(90)cos⁡(a)tan⁡(a)tan⁡(270)tan⁡(a)+1−sin⁡(90)sin⁡(a)cos⁡(180)cos⁡(a)tan⁡(270)tan⁡(270)tan⁡(a)+1+sin⁡(180)sin⁡(a)cos⁡(90)cos⁡(a)tan⁡(270)tan⁡(270)tan⁡(a)+1−sin⁡(90)sin⁡(180)cos⁡2(a)tan⁡(a)tan⁡(270)tan⁡(a)+1+sin⁡(90)sin⁡(180)cos⁡2(a)tan⁡(270)tan⁡(270)tan⁡(a)+1−sin⁡2(a)cos⁡(90)cos⁡(180)tan⁡(a)−tan⁡(180)tan⁡(a)+1−sin⁡2(a)cos⁡(90)cos⁡(180)tan⁡(180)−tan⁡(180)tan⁡(a)+1+sin⁡(180)sin⁡(a)cos⁡(90)cos⁡(a)tan⁡(a)−tan⁡(180)tan⁡(a)+1−sin⁡(90)sin⁡(a)cos⁡(180)cos⁡(a)tan⁡(a)−tan⁡(180)tan⁡(a)+1+sin⁡(180)sin⁡(a)cos⁡(90)cos⁡(a)tan⁡(180)−tan⁡(180)tan⁡(a)+1−sin⁡(90)sin⁡(a)cos⁡(180)cos⁡(a)tan⁡(180)−tan⁡(180)tan⁡(a)+1+sin⁡(90)sin⁡(180)cos⁡2(a)tan⁡(a)−tan⁡(180)tan⁡(a)+1+sin⁡(90)sin⁡(180)cos⁡2(a)tan⁡(180)−tan⁡(180)tan⁡(a)+1\frac{\sin^{2}{\left(a \right)} \cos{\left(90 \right)} \cos{\left(180 \right)} \tan{\left(a \right)}}{\tan{\left(270 \right)} \tan{\left(a \right)} + 1} - \frac{\sin^{2}{\left(a \right)} \cos{\left(90 \right)} \cos{\left(180 \right)} \tan{\left(270 \right)}}{\tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{\sin{\left(90 \right)} \sin{\left(a \right)} \cos{\left(180 \right)} \cos{\left(a \right)} \tan{\left(a \right)}}{\tan{\left(270 \right)} \tan{\left(a \right)} + 1} - \frac{\sin{\left(180 \right)} \sin{\left(a \right)} \cos{\left(90 \right)} \cos{\left(a \right)} \tan{\left(a \right)}}{\tan{\left(270 \right)} \tan{\left(a \right)} + 1} - \frac{\sin{\left(90 \right)} \sin{\left(a \right)} \cos{\left(180 \right)} \cos{\left(a \right)} \tan{\left(270 \right)}}{\tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{\sin{\left(180 \right)} \sin{\left(a \right)} \cos{\left(90 \right)} \cos{\left(a \right)} \tan{\left(270 \right)}}{\tan{\left(270 \right)} \tan{\left(a \right)} + 1} - \frac{\sin{\left(90 \right)} \sin{\left(180 \right)} \cos^{2}{\left(a \right)} \tan{\left(a \right)}}{\tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{\sin{\left(90 \right)} \sin{\left(180 \right)} \cos^{2}{\left(a \right)} \tan{\left(270 \right)}}{\tan{\left(270 \right)} \tan{\left(a \right)} + 1} - \frac{\sin^{2}{\left(a \right)} \cos{\left(90 \right)} \cos{\left(180 \right)} \tan{\left(a \right)}}{- \tan{\left(180 \right)} \tan{\left(a \right)} + 1} - \frac{\sin^{2}{\left(a \right)} \cos{\left(90 \right)} \cos{\left(180 \right)} \tan{\left(180 \right)}}{- \tan{\left(180 \right)} \tan{\left(a \right)} + 1} + \frac{\sin{\left(180 \right)} \sin{\left(a \right)} \cos{\left(90 \right)} \cos{\left(a \right)} \tan{\left(a \right)}}{- \tan{\left(180 \right)} \tan{\left(a \right)} + 1} - \frac{\sin{\left(90 \right)} \sin{\left(a \right)} \cos{\left(180 \right)} \cos{\left(a \right)} \tan{\left(a \right)}}{- \tan{\left(180 \right)} \tan{\left(a \right)} + 1} + \frac{\sin{\left(180 \right)} \sin{\left(a \right)} \cos{\left(90 \right)} \cos{\left(a \right)} \tan{\left(180 \right)}}{- \tan{\left(180 \right)} \tan{\left(a \right)} + 1} - \frac{\sin{\left(90 \right)} \sin{\left(a \right)} \cos{\left(180 \right)} \cos{\left(a \right)} \tan{\left(180 \right)}}{- \tan{\left(180 \right)} \tan{\left(a \right)} + 1} + \frac{\sin{\left(90 \right)} \sin{\left(180 \right)} \cos^{2}{\left(a \right)} \tan{\left(a \right)}}{- \tan{\left(180 \right)} \tan{\left(a \right)} + 1} + \frac{\sin{\left(90 \right)} \sin{\left(180 \right)} \cos^{2}{\left(a \right)} \tan{\left(180 \right)}}{- \tan{\left(180 \right)} \tan{\left(a \right)} + 1}