Калькуляторы онлайн/ Решение уравнений/ Упрощение выражений/ 2563*(sin(2*x)/2+x)/800-35*(x-sin(2*x)/2)/2-2563*sin(x)/200+211*cos(x)^2/25-422*cos(x)/25+2563*x/400 если x=2

2563*(sin(2*x)/2+x)/800-3 ... x)/25+2563*x/400 если x=2 (упростите выражение)

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Вы ввели [src]
     /sin(2*x)    \      /    sin(2*x)\                                                  
2563*|-------- + x|   35*|x - --------|                        2                         
     \   2        /      \       2    /   2563*sin(x)   211*cos (x)   422*cos(x)   2563*x
------------------- - ----------------- - ----------- + ----------- - ---------- + ------
        800                   2               200            25           25        400
2563x400+−35x2−354sin⁡(2x)+2563800(x+12sin⁡(2x))−2563200sin⁡(x)+21125cos⁡2(x)−42225cos⁡(x)\frac{2563 x}{400} + - \frac{35 x}{2} - \frac{35}{4} \sin{\left (2 x \right )} + \frac{2563}{800} \left(x + \frac{1}{2} \sin{\left (2 x \right )}\right) - \frac{2563}{200} \sin{\left (x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}
Подстановка условия [src]
(2563*(sin(2*x)/2 + x))/800 - 35*(x - sin(2*x)/2)/2 - 2563*sin(x)/200 + (211*cos(x)^2)/25 - 422*cos(x)/25 + (2563*x)/400 при x = 2
(2563*(sin(2*x)/2 + x))/800 - 35*(x - sin(2*x)/2)/2 - 2563*sin(x)/200 + (211*cos(x)^2)/25 - 422*cos(x)/25 + (2563*x)/400
2563x400+−35x2−354sin⁡(2x)+2563800(x+12sin⁡(2x))−2563200sin⁡(x)+21125cos⁡2(x)−42225cos⁡(x)\frac{2563 x}{400} + - \frac{35 x}{2} - \frac{35}{4} \sin{\left (2 x \right )} + \frac{2563}{800} \left(x + \frac{1}{2} \sin{\left (2 x \right )}\right) - \frac{2563}{200} \sin{\left (x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}
(2563*(sin(2*(2))/2 + (2)))/800 - 35*((2) - sin(2*(2))/2)/2 - 2563*sin((2))/200 + (211*cos((2))^2)/25 - 422*cos((2))/25 + (2563*(2))/400
2563(2)400+−35(2)2−354sin⁡(2(2))+2563800((2)+12sin⁡(2(2)))−2563200sin⁡((2))+21125cos⁡2((2))−42225cos⁡((2))\frac{2563 (2)}{400} + - \frac{35 (2)}{2} - \frac{35}{4} \sin{\left (2 (2) \right )} + \frac{2563}{800} \left((2) + \frac{1}{2} \sin{\left (2 (2) \right )}\right) - \frac{2563}{200} \sin{\left ((2) \right )} + \frac{211}{25} \cos^{2}{\left ((2) \right )} - \frac{422}{25} \cos{\left ((2) \right )}
(2563*(sin(2*2)/2 + 2))/800 - 35*(2 - sin(2*2)/2)/2 - 2563*sin(2)/200 + (211*cos(2)^2)/25 - 422*cos(2)/25 + (2563*2)/400
−−354sin⁡(2⋅2)+35+2563800(12sin⁡(2⋅2)+2)−2563200sin⁡(2)+21125cos⁡2(2)−42225cos⁡(2)+51264001- - \frac{35}{4} \sin{\left (2 \cdot 2 \right )} + 35 + \frac{2563}{800} \left(\frac{1}{2} \sin{\left (2 \cdot 2 \right )} + 2\right) - \frac{2563}{200} \sin{\left (2 \right )} + \frac{211}{25} \cos^{2}{\left (2 \right )} - \frac{422}{25} \cos{\left (2 \right )} + \frac{5126}{400} 1
-6311/400 - 2563*sin(2)/200 - 422*cos(2)/25 + 211*cos(2)^2/25 + 16563*sin(4)/1600
−6311400−2563200sin⁡(2)+165631600sin⁡(4)+21125cos⁡2(2)−42225cos⁡(2)- \frac{6311}{400} - \frac{2563}{200} \sin{\left (2 \right )} + \frac{16563}{1600} \sin{\left (4 \right )} + \frac{211}{25} \cos^{2}{\left (2 \right )} - \frac{422}{25} \cos{\left (2 \right )}
Степени [src]
                                             2                    
  6311*x   2563*sin(x)   422*cos(x)   211*cos (x)   16563*sin(2*x)
- ------ - ----------- - ---------- + ----------- + --------------
   800         200           25            25            1600
−6311x800−2563200sin⁡(x)+165631600sin⁡(2x)+21125cos⁡2(x)−42225cos⁡(x)- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}
Численный ответ [src]
10.351875*sin(2*x) + 8.44*cos(x)^2 - 7.88875*x - 16.88*cos(x) - 12.815*sin(x)
Рациональный знаменатель [src]
                                             2                    
  6311*x   2563*sin(x)   422*cos(x)   211*cos (x)   16563*sin(2*x)
- ------ - ----------- - ---------- + ----------- + --------------
   800         200           25            25            1600
−6311x800−2563200sin⁡(x)+165631600sin⁡(2x)+21125cos⁡2(x)−42225cos⁡(x)- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}
Объединение рациональных выражений [src]
                                                  2                    
-27008*cos(x) - 20504*sin(x) - 12622*x + 13504*cos (x) + 16563*sin(2*x)
-----------------------------------------------------------------------
                                  1600
11600(−12622x−20504sin⁡(x)+16563sin⁡(2x)+13504cos⁡2(x)−27008cos⁡(x))\frac{1}{1600} \left(- 12622 x - 20504 \sin{\left (x \right )} + 16563 \sin{\left (2 x \right )} + 13504 \cos^{2}{\left (x \right )} - 27008 \cos{\left (x \right )}\right)
Общее упрощение [src]
                                             2                    
  6311*x   2563*sin(x)   422*cos(x)   211*cos (x)   16563*sin(2*x)
- ------ - ----------- - ---------- + ----------- + --------------
   800         200           25            25            1600
−6311x800−2563200sin⁡(x)+165631600sin⁡(2x)+21125cos⁡2(x)−42225cos⁡(x)- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}
Собрать выражение [src]
                            /sin(2*x)    \      /    sin(2*x)\                           
       2               2563*|-------- + x|   35*|x - --------|                           
211*cos (x)   2563*x        \   2        /      \       2    /   422*cos(x)   2563*sin(x)
----------- + ------ + ------------------- - ----------------- - ---------- - -----------
     25        400             800                   2               25           200
2563x400−35x2−354sin⁡(2x)+2563800(x+12sin⁡(2x))−2563200sin⁡(x)−42225cos⁡(x)+21125cos⁡2(x)\frac{2563 x}{400} - \frac{35 x}{2} - \frac{35}{4} \sin{\left (2 x \right )} + \frac{2563}{800} \left(x + \frac{1}{2} \sin{\left (2 x \right )}\right) - \frac{2563}{200} \sin{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )}
211   6311*x   2563*sin(x)   422*cos(x)   211*cos(2*x)   16563*sin(2*x)
--- - ------ - ----------- - ---------- + ------------ + --------------
 50    800         200           25            50             1600
−6311x800−2563200sin⁡(x)+165631600sin⁡(2x)−42225cos⁡(x)+21150cos⁡(2x)+21150- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} - \frac{422}{25} \cos{\left (x \right )} + \frac{211}{50} \cos{\left (2 x \right )} + \frac{211}{50}
Общий знаменатель [src]
                                             2                    
  6311*x   2563*sin(x)   422*cos(x)   211*cos (x)   16563*sin(2*x)
- ------ - ----------- - ---------- + ----------- + --------------
   800         200           25            25            1600
−6311x800−2563200sin⁡(x)+165631600sin⁡(2x)+21125cos⁡2(x)−42225cos⁡(x)- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}
Комбинаторика [src]
 /                           2                                           \ 
-\-16563*sin(2*x) - 13504*cos (x) + 12622*x + 20504*sin(x) + 27008*cos(x)/ 
---------------------------------------------------------------------------
                                    1600
−11600(12622x+20504sin⁡(x)−16563sin⁡(2x)−13504cos⁡2(x)+27008cos⁡(x))- \frac{1}{1600} \left(12622 x + 20504 \sin{\left (x \right )} - 16563 \sin{\left (2 x \right )} - 13504 \cos^{2}{\left (x \right )} + 27008 \cos{\left (x \right )}\right)
Тригонометрическая часть [src]
211   6311*x   2563*sin(x)   422*cos(x)   211*cos(2*x)   16563*sin(2*x)
--- - ------ - ----------- - ---------- + ------------ + --------------
 50    800         200           25            50             1600
−6311x800−2563200sin⁡(x)+165631600sin⁡(2x)−42225cos⁡(x)+21150cos⁡(2x)+21150- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} - \frac{422}{25} \cos{\left (x \right )} + \frac{211}{50} \cos{\left (2 x \right )} + \frac{211}{50}
Раскрыть выражение [src]
                                             2                         
  6311*x   2563*sin(x)   422*cos(x)   211*cos (x)   16563*cos(x)*sin(x)
- ------ - ----------- - ---------- + ----------- + -------------------
   800         200           25            25               800
−6311x800+16563800sin⁡(x)cos⁡(x)−2563200sin⁡(x)+21125cos⁡2(x)−42225cos⁡(x)- \frac{6311 x}{800} + \frac{16563}{800} \sin{\left (x \right )} \cos{\left (x \right )} - \frac{2563}{200} \sin{\left (x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}