Дано
$$x cos{left (2 right )} + x sin{left (2 right )} – 1 + left(- sin{left (x right )} + 1right) left(sin{left (x right )} + 1right)$$
Подстановка условия
$$x cos{left (2 right )} + x sin{left (2 right )} – 1 + left(- sin{left (x right )} + 1right) left(sin{left (x right )} + 1right)$$
sin(2)*(-1/2) – 1 + cos(2)*(-1/2) + (1 – sin((-1/2)))*(1 + sin((-1/2)))
$$(-1/2) cos{left (2 right )} + (-1/2) sin{left (2 right )} – 1 + left(- sin{left ((-1/2) right )} + 1right) left(sin{left ((-1/2) right )} + 1right)$$
sin(2)*(-1)/2 – 1 + cos(2)*(-1)/2 + (1 – sin(-1/2))*(1 + sin(-1/2))
$$-1 + frac{1}{2} left(-1 sin{left (2 right )}right) + frac{1}{2} left(-1 cos{left (2 right )}right) + left(- sin{left (- frac{1}{2} right )} + 1right) left(sin{left (- frac{1}{2} right )} + 1right)$$
-1 – cos(2)/2 – sin(2)/2 + (1 – sin(1/2))*(1 + sin(1/2))
$$-1 – frac{1}{2} sin{left (2 right )} – frac{1}{2} cos{left (2 right )} + left(- sin{left (frac{1}{2} right )} + 1right) left(sin{left (frac{1}{2} right )} + 1right)$$
Степени
$$x cos{left (2 right )} + x sin{left (2 right )} + left(- sin{left (x right )} + 1right) left(sin{left (x right )} + 1right) – 1$$
Численный ответ
-1.0 + 0.493150590278539*x + (1.0 – sin(x))*(1.0 + sin(x))
Рациональный знаменатель
$$x cos{left (2 right )} + x sin{left (2 right )} + left(- sin{left (x right )} + 1right) left(sin{left (x right )} + 1right) – 1$$
Объединение рациональных выражений
$$x cos{left (2 right )} + x sin{left (2 right )} + left(- sin{left (x right )} + 1right) left(sin{left (x right )} + 1right) – 1$$
Общее упрощение
2 ___ / pi
– sin (x) + x*/ 2 *sin|2 + –|
4 /
$$sqrt{2} x sin{left (frac{pi}{4} + 2 right )} – sin^{2}{left (x right )}$$
Соберем выражение
$$x cos{left (2 right )} + x sin{left (2 right )} + left(- sin{left (x right )} + 1right) left(sin{left (x right )} + 1right) – 1$$
1 cos(2*x)
– – + ——– + x*cos(2) + x*sin(2)
2 2
$$x cos{left (2 right )} + x sin{left (2 right )} + frac{1}{2} cos{left (2 x right )} – frac{1}{2}$$
Общий знаменатель
2
– sin (x) + x*cos(2) + x*sin(2)
$$x cos{left (2 right )} + x sin{left (2 right )} – sin^{2}{left (x right )}$$
Тригонометрическая часть
2 ___ / pi
– sin (x) + x*/ 2 *sin|2 + –|
4 /
$$sqrt{2} x sin{left (frac{pi}{4} + 2 right )} – sin^{2}{left (x right )}$$
Комбинаторика
2
– sin (x) + x*cos(2) + x*sin(2)
$$x cos{left (2 right )} + x sin{left (2 right )} – sin^{2}{left (x right )}$$
Раскрыть выражение
-1 + x*cos(2) + x*sin(2) + (1 – sin(x))*(1 + sin(x))
$$x cos{left (2 right )} + x sin{left (2 right )} + left(- sin{left (x right )} + 1right) left(sin{left (x right )} + 1right) – 1$$