8*(1+tan(x)^2)*(2+3*tan(x)^2)*tan(x) если x=-4 (упростите выражение)

Вы ввели

  /       2   \ /         2   \       
8*\1 + tan (x)/*\2 + 3*tan (x)/*tan(x)

$$8 \left(\tan^{2}{\left (x \right )} + 1\right) \left(3 \tan^{2}{\left (x \right )} + 2\right) \tan{\left (x \right )}$$

Подстановка условия

((8*(1 + tan(x)^2))*(2 + 3*tan(x)^2))*tan(x) при x = -4

((8*(1 + tan(x)^2))*(2 + 3*tan(x)^2))*tan(x)

$$8 \left(\tan^{2}{\left (x \right )} + 1\right) \left(3 \tan^{2}{\left (x \right )} + 2\right) \tan{\left (x \right )}$$

((8*(1 + tan((-4))^2))*(2 + 3*tan((-4))^2))*tan((-4))

$$8 \left(\tan^{2}{\left ((-4) \right )} + 1\right) \left(3 \tan^{2}{\left ((-4) \right )} + 2\right) \tan{\left ((-4) \right )}$$

((8*(1 + tan(-4)^2))*(2 + 3*tan(-4)^2))*tan(-4)

$$8 \left(1 + \tan^{2}{\left (-4 \right )}\right) \left(2 + 3 \tan^{2}{\left (-4 \right )}\right) \tan{\left (-4 \right )}$$

-(2 + 3*tan(4)^2)*(8 + 8*tan(4)^2)*tan(4)

$$- \left(2 + 3 \tan^{2}{\left (4 \right )}\right) \left(8 + 8 \tan^{2}{\left (4 \right )}\right) \tan{\left (4 \right )}$$

Степени

/         2   \ /         2   \       
\2 + 3*tan (x)/*\8 + 8*tan (x)/*tan(x)

$$\left(3 \tan^{2}{\left (x \right )} + 2\right) \left(8 \tan^{2}{\left (x \right )} + 8\right) \tan{\left (x \right )}$$

Численный ответ

8.0*(1.0 + tan(x)^2)*(2.0 + 3.0*tan(x)^2)*tan(x)

Рациональный знаменатель

/         2   \ /         2   \       
\2 + 3*tan (x)/*\8 + 8*tan (x)/*tan(x)

$$\left(3 \tan^{2}{\left (x \right )} + 2\right) \left(8 \tan^{2}{\left (x \right )} + 8\right) \tan{\left (x \right )}$$

Объединение рациональных выражений

/         2   \ /         2   \       
\2 + 3*tan (x)/*\8 + 8*tan (x)/*tan(x)

$$\left(3 \tan^{2}{\left (x \right )} + 2\right) \left(8 \tan^{2}{\left (x \right )} + 8\right) \tan{\left (x \right )}$$

Общее упрощение

                  5            3   
16*tan(x) + 24*tan (x) + 40*tan (x)

$$24 \tan^{5}{\left (x \right )} + 40 \tan^{3}{\left (x \right )} + 16 \tan{\left (x \right )}$$

Собрать выражение

  /     2           2       2   \       
8*\2*sec (x) + 3*sec (x)*tan (x)/*tan(x)

$$8 \left(3 \tan^{2}{\left (x \right )} \sec^{2}{\left (x \right )} + 2 \sec^{2}{\left (x \right )}\right) \tan{\left (x \right )}$$

/         2   \ /         2   \       
\2 + 3*tan (x)/*\8 + 8*tan (x)/*tan(x)

$$\left(3 \tan^{2}{\left (x \right )} + 2\right) \left(8 \tan^{2}{\left (x \right )} + 8\right) \tan{\left (x \right )}$$

Общий знаменатель

                  5            3   
16*tan(x) + 24*tan (x) + 40*tan (x)

$$24 \tan^{5}{\left (x \right )} + 40 \tan^{3}{\left (x \right )} + 16 \tan{\left (x \right )}$$

Тригонометрическая часть

  /         2   \       
8*\2 + 3*tan (x)/*tan(x)
------------------------
           2            
        cos (x)         

$$\frac{8 \tan{\left (x \right )}}{\cos^{2}{\left (x \right )}} \left(3 \tan^{2}{\left (x \right )} + 2\right)$$