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cos(90+x)*tan(270+x)/cos( ... 0-x)*sin(90-x) если x=3/2 (упростите выражение)

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Примеры

Решение

Вы ввели [src]
cos(90 + x)*tan(270 + x)            
------------------------*sin(90 - x)
      cos(180 - x)
$$\frac{\cos{\left (x + 90 \right )} \tan{\left (x + 270 \right )}}{\cos{\left (- x + 180 \right )}} \sin{\left (- x + 90 \right )}$$
Подстановка условия [src]
((cos(90 + x)*tan(270 + x))/cos(180 - x))*sin(90 - x) при x = 3/2
((cos(90 + x)*tan(270 + x))/cos(180 - x))*sin(90 - x)
$$\frac{\cos{\left (x + 90 \right )} \tan{\left (x + 270 \right )}}{\cos{\left (- x + 180 \right )}} \sin{\left (- x + 90 \right )}$$
((cos(90 + (3/2))*tan(270 + (3/2)))/cos(180 - (3/2)))*sin(90 - (3/2))
$$\frac{\cos{\left ((3/2) + 90 \right )} \tan{\left ((3/2) + 270 \right )}}{\cos{\left (- (3/2) + 180 \right )}} \sin{\left (- (3/2) + 90 \right )}$$
((cos(90 + 3/2)*tan(270 + 3/2))/cos(180 - 3/2))*sin(90 - 3/2)
$$\frac{\cos{\left (\frac{3}{2} + 90 \right )} \tan{\left (\frac{3}{2} + 270 \right )}}{\cos{\left (- \frac{3}{2} + 180 \right )}} \sin{\left (- \frac{3}{2} + 90 \right )}$$
cos(183/2)*sin(177/2)*tan(543/2)/cos(357/2)
$$\frac{\sin{\left (\frac{177}{2} \right )} \cos{\left (\frac{183}{2} \right )}}{\cos{\left (\frac{357}{2} \right )}} \tan{\left (\frac{543}{2} \right )}$$
Степени [src]
-cos(90 + x)*sin(-90 + x)*tan(270 + x) 
---------------------------------------
             cos(-180 + x)
$$- \frac{\sin{\left (x - 90 \right )} \cos{\left (x + 90 \right )}}{\cos{\left (x - 180 \right )}} \tan{\left (x + 270 \right )}$$
Численный ответ [src]
cos(90 + x)*sin(90 - x)*tan(270 + x)/cos(180 - x)
Рациональный знаменатель [src]
-cos(90 + x)*sin(-90 + x)*tan(270 + x) 
---------------------------------------
             cos(-180 + x)
$$- \frac{\sin{\left (x - 90 \right )} \cos{\left (x + 90 \right )}}{\cos{\left (x - 180 \right )}} \tan{\left (x + 270 \right )}$$
Объединение рациональных выражений [src]
-cos(90 + x)*sin(-90 + x)*tan(270 + x) 
---------------------------------------
             cos(-180 + x)
$$- \frac{\sin{\left (x - 90 \right )} \cos{\left (x + 90 \right )}}{\cos{\left (x - 180 \right )}} \tan{\left (x + 270 \right )}$$
Общее упрощение [src]
-cos(90 + x)*sin(-90 + x)*tan(270 + x) 
---------------------------------------
             cos(-180 + x)
$$- \frac{\sin{\left (x - 90 \right )} \cos{\left (x + 90 \right )}}{\cos{\left (x - 180 \right )}} \tan{\left (x + 270 \right )}$$
Собрать выражение [src]
 /sin(2*x)   sin(180)\                           
-|-------- - --------|*sec(-180 + x)*tan(270 + x)
 \   2          2    /
$$- \left(\frac{1}{2} \sin{\left (2 x \right )} - \frac{1}{2} \sin{\left (180 \right )}\right) \tan{\left (x + 270 \right )} \sec{\left (x - 180 \right )}$$
cos(90 + x)*sin(90 - x)*tan(270 + x)
------------------------------------
            cos(180 - x)
$$\frac{\sin{\left (- x + 90 \right )} \cos{\left (x + 90 \right )}}{\cos{\left (- x + 180 \right )}} \tan{\left (x + 270 \right )}$$
Общий знаменатель [src]
cos(90 + x)*sin(90 - x)*tan(270 + x)
------------------------------------
            cos(180 - x)
$$\frac{\sin{\left (- x + 90 \right )} \cos{\left (x + 90 \right )}}{\cos{\left (- x + 180 \right )}} \tan{\left (x + 270 \right )}$$
Тригонометрическая часть [src]
cos(90 + x)*sin(90 - x)*tan(270 + x)
------------------------------------
           cos(-180 + x)
$$\frac{\cos{\left (x + 90 \right )} \tan{\left (x + 270 \right )}}{\cos{\left (x - 180 \right )}} \sin{\left (- x + 90 \right )}$$
Комбинаторика [src]
-cos(90 + x)*sin(-90 + x)*tan(270 + x) 
---------------------------------------
             cos(-180 + x)
$$- \frac{\sin{\left (x - 90 \right )} \cos{\left (x + 90 \right )}}{\cos{\left (x - 180 \right )}} \tan{\left (x + 270 \right )}$$
Раскрыть выражение [src]
-(cos(90)*cos(x) - sin(90)*sin(x))*(cos(90)*sin(x) - cos(x)*sin(90))*(tan(270) + tan(x)) 
-----------------------------------------------------------------------------------------
                (1 - tan(270)*tan(x))*(cos(180)*cos(x) + sin(180)*sin(x))
$$- \frac{\left(- \sin{\left (90 \right )} \sin{\left (x \right )} + \cos{\left (90 \right )} \cos{\left (x \right )}\right) \left(\sin{\left (x \right )} \cos{\left (90 \right )} - \sin{\left (90 \right )} \cos{\left (x \right )}\right) \left(\tan{\left (x \right )} + \tan{\left (270 \right )}\right)}{\left(\sin{\left (180 \right )} \sin{\left (x \right )} + \cos{\left (180 \right )} \cos{\left (x \right )}\right) \left(- \tan{\left (270 \right )} \tan{\left (x \right )} + 1\right)}$$