-2*i*sin(t)^2-2*i*cos(t)^ ... t)^2+k*cos(t) если i=-3/2 (упростите выражение)

Вы ввели

        2             2                        2           2              
-2*I*sin (t) - 2*I*cos (t) + 2*u*sin(t) - k*sin (t) - k*cos (t) + k*cos(t)

$$k \cos{\left (t \right )} + - k \cos^{2}{\left (t \right )} + - k \sin^{2}{\left (t \right )} + 2 u \sin{\left (t \right )} + - 2 i \sin^{2}{\left (t \right )} - 2 i \cos^{2}{\left (t \right )}$$

Подстановка условия

(-2*i)*sin(t)^2 - 2*i*cos(t)^2 + (2*u)*sin(t) - k*sin(t)^2 - k*cos(t)^2 + k*cos(t) при False

(-2*i)*sin(t)^2 - 2*i*cos(t)^2 + (2*u)*sin(t) - k*sin(t)^2 - k*cos(t)^2 + k*cos(t)

$$k \cos{\left (t \right )} + - k \cos^{2}{\left (t \right )} + - k \sin^{2}{\left (t \right )} + 2 u \sin{\left (t \right )} + - 2 i \sin^{2}{\left (t \right )} - 2 i \cos^{2}{\left (t \right )}$$

(-2*(-3/2))*sin(t)^2 - 2*(-3/2)*cos(t)^2 + (2*u)*sin(t) - k*sin(t)^2 - k*cos(t)^2 + k*cos(t)

$$k \cos{\left (t \right )} + - k \cos^{2}{\left (t \right )} + - k \sin^{2}{\left (t \right )} + 2 u \sin{\left (t \right )} + - 2 (-3/2) \sin^{2}{\left (t \right )} - 2 (-3/2) \cos^{2}{\left (t \right )}$$

(-(-3))*sin(t)^2 - 2*(-3)/2*cos(t)^2 + (2*u)*sin(t) - k*sin(t)^2 - k*cos(t)^2 + k*cos(t)

$$k \cos{\left (t \right )} + - k \cos^{2}{\left (t \right )} + - k \sin^{2}{\left (t \right )} + 2 u \sin{\left (t \right )} + - -3 \sin^{2}{\left (t \right )} - - 3 \cos^{2}{\left (t \right )}$$

3*cos(t)^2 + 3*sin(t)^2 + k*cos(t) - k*cos(t)^2 - k*sin(t)^2 + 2*u*sin(t)

$$- k \sin^{2}{\left (t \right )} - k \cos^{2}{\left (t \right )} + k \cos{\left (t \right )} + 2 u \sin{\left (t \right )} + 3 \sin^{2}{\left (t \right )} + 3 \cos^{2}{\left (t \right )}$$

Степени

                2           2             2             2                
k*cos(t) - k*cos (t) - k*sin (t) - 2*I*cos (t) - 2*I*sin (t) + 2*u*sin(t)

$$- k \sin^{2}{\left (t \right )} - k \cos^{2}{\left (t \right )} + k \cos{\left (t \right )} + 2 u \sin{\left (t \right )} - 2 i \sin^{2}{\left (t \right )} - 2 i \cos^{2}{\left (t \right )}$$

Численный ответ

k*cos(t) - k*cos(t)^2 - k*sin(t)^2 + 2.0*u*sin(t) - 2.0*i*cos(t)^2 - 2.0*i*sin(t)^2

Рациональный знаменатель

                2           2             2             2                
k*cos(t) - k*cos (t) - k*sin (t) - 2*I*cos (t) - 2*I*sin (t) + 2*u*sin(t)

$$- k \sin^{2}{\left (t \right )} - k \cos^{2}{\left (t \right )} + k \cos{\left (t \right )} + 2 u \sin{\left (t \right )} - 2 i \sin^{2}{\left (t \right )} - 2 i \cos^{2}{\left (t \right )}$$

Объединение рациональных выражений

                2           2          /     2         2   \             
k*cos(t) - k*cos (t) - k*sin (t) + 2*I*\- cos (t) - sin (t)/ + 2*u*sin(t)

$$- k \sin^{2}{\left (t \right )} - k \cos^{2}{\left (t \right )} + k \cos{\left (t \right )} + 2 u \sin{\left (t \right )} + 2 i \left(- \sin^{2}{\left (t \right )} - \cos^{2}{\left (t \right )}\right)$$

Общее упрощение

-k - 2*I + k*cos(t) + 2*u*sin(t)

$$k \cos{\left (t \right )} - k + 2 u \sin{\left (t \right )} - 2 i$$

Собрать выражение

-k - 2*I + k*cos(t) + 2*u*sin(t)

$$k \cos{\left (t \right )} - k + 2 u \sin{\left (t \right )} - 2 i$$

                   2                        2           2             2   
k*cos(t) + -2*I*sin (t) + 2*u*sin(t) - k*cos (t) - k*sin (t) - 2*I*cos (t)

$$- k \sin^{2}{\left (t \right )} - k \cos^{2}{\left (t \right )} + k \cos{\left (t \right )} + 2 u \sin{\left (t \right )} + - 2 i \sin^{2}{\left (t \right )} - 2 i \cos^{2}{\left (t \right )}$$

Комбинаторика

                2           2             2             2                
k*cos(t) - k*cos (t) - k*sin (t) - 2*I*cos (t) - 2*I*sin (t) + 2*u*sin(t)

$$- k \sin^{2}{\left (t \right )} - k \cos^{2}{\left (t \right )} + k \cos{\left (t \right )} + 2 u \sin{\left (t \right )} - 2 i \sin^{2}{\left (t \right )} - 2 i \cos^{2}{\left (t \right )}$$

Общий знаменатель

                2           2             2             2                
k*cos(t) - k*cos (t) - k*sin (t) - 2*I*cos (t) - 2*I*sin (t) + 2*u*sin(t)

$$- k \sin^{2}{\left (t \right )} - k \cos^{2}{\left (t \right )} + k \cos{\left (t \right )} + 2 u \sin{\left (t \right )} - 2 i \sin^{2}{\left (t \right )} - 2 i \cos^{2}{\left (t \right )}$$

Тригонометрическая часть

-k - 2*I + k*cos(t) + 2*u*sin(t)

$$k \cos{\left (t \right )} - k + 2 u \sin{\left (t \right )} - 2 i$$

Раскрыть выражение

                2           2             2             2                
k*cos(t) - k*cos (t) - k*sin (t) - 2*I*cos (t) - 2*I*sin (t) + 2*u*sin(t)

$$- k \sin^{2}{\left (t \right )} - k \cos^{2}{\left (t \right )} + k \cos{\left (t \right )} + 2 u \sin{\left (t \right )} - 2 i \sin^{2}{\left (t \right )} - 2 i \cos^{2}{\left (t \right )}$$