Дано
$$sqrt{3 sin{left (x right )}} + sqrt{3 cos{left (2 x right )}} + frac{sin{left (2 x right )}}{cos{left (x right )}}$$
Подстановка условия
$$sqrt{3 sin{left (x right )}} + sqrt{3 cos{left (2 x right )}} + frac{sin{left (2 x right )}}{cos{left (x right )}}$$
sqrt(3*cos(2*(-4))) + sin(2*(-4))/cos((-4)) + sqrt(3*sin((-4)))
$$sqrt{3 sin{left ((-4) right )}} + sqrt{3 cos{left (2 (-4) right )}} + frac{sin{left (2 (-4) right )}}{cos{left ((-4) right )}}$$
sqrt(3*cos(2*(-4))) + sin(2*(-4))/cos(-4) + sqrt(3*sin(-4))
$$sqrt{3 sin{left (-4 right )}} + frac{sin{left (-4 cdot 2 right )}}{cos{left (-4 right )}} + sqrt{3 cos{left (-4 cdot 2 right )}}$$
sqrt(3)*sqrt(-sin(4)) + sqrt(3)*sqrt(cos(8)) – sin(8)/cos(4)
$$sqrt{3} sqrt{- sin{left (4 right )}} – frac{sin{left (8 right )}}{cos{left (4 right )}} + sqrt{3} sqrt{cos{left (8 right )}}$$
Степени
$$sqrt{3} sqrt{sin{left (x right )}} + frac{sin{left (2 x right )}}{cos{left (x right )}} + sqrt{3} sqrt{cos{left (2 x right )}}$$
Численный ответ
1.73205080756888*cos(2*x)^0.5 + 1.73205080756888*sin(x)^0.5 + sin(2*x)/cos(x)
Рациональный знаменатель
$$frac{1}{cos{left (x right )}} left(sqrt{3} sqrt{sin{left (x right )}} cos{left (x right )} + sin{left (2 x right )} + sqrt{3} cos{left (x right )} sqrt{cos{left (2 x right )}}right)$$
Объединение рациональных выражений
$$frac{1}{cos{left (x right )}} left(sqrt{3} sqrt{sin{left (x right )}} cos{left (x right )} + sin{left (2 x right )} + sqrt{3} cos{left (x right )} sqrt{cos{left (2 x right )}}right)$$
Общее упрощение
___ __________ ___ ________
2*sin(x) + / 3 */ cos(2*x) + / 3 */ sin(x)
$$sqrt{3} sqrt{sin{left (x right )}} + 2 sin{left (x right )} + sqrt{3} sqrt{cos{left (2 x right )}}$$
Соберем выражение
$$sqrt{3 cos{left (2 x right )}} + sqrt{3} sqrt{sin{left (x right )}} + frac{sin{left (2 x right )}}{cos{left (x right )}}$$
___ __________ ___ ________
/ 3 */ cos(2*x) + / 3 */ sin(x) + sec(x)*sin(2*x)
$$sqrt{3} sqrt{sin{left (x right )}} + sin{left (2 x right )} sec{left (x right )} + sqrt{3} sqrt{cos{left (2 x right )}}$$
Общий знаменатель
___ __________ ___ ________ sin(2*x)
/ 3 */ cos(2*x) + / 3 */ sin(x) + ——–
cos(x)
$$sqrt{3} sqrt{sin{left (x right )}} + frac{sin{left (2 x right )}}{cos{left (x right )}} + sqrt{3} sqrt{cos{left (2 x right )}}$$
Тригонометрическая часть
____________ __________
/ 3*cos(2*x) + / 3*sin(x) + 2*sin(x)
$$sqrt{3 sin{left (x right )}} + sqrt{3 cos{left (2 x right )}} + 2 sin{left (x right )}$$
Комбинаторика
___ __________ ___ ________
/ 3 */ cos(2*x) *cos(x) + / 3 */ sin(x) *cos(x) + sin(2*x)
————————————————————–
cos(x)
$$frac{1}{cos{left (x right )}} left(sqrt{3} sqrt{sin{left (x right )}} cos{left (x right )} + sin{left (2 x right )} + sqrt{3} cos{left (x right )} sqrt{cos{left (2 x right )}}right)$$
Раскрыть выражение
___ __________ ___ ________ sin(2*x)
/ 3 */ cos(2*x) + / 3 */ sin(x) + ——–
cos(x)
$$sqrt{3} sqrt{sin{left (x right )}} + frac{sin{left (2 x right )}}{cos{left (x right )}} + sqrt{3} sqrt{cos{left (2 x right )}}$$
___________________
___ / 2 2 ___ ________
2*sin(x) + / 3 */ cos (x) – sin (x) + / 3 */ sin(x)
$$sqrt{3} sqrt{- sin^{2}{left (x right )} + cos^{2}{left (x right )}} + sqrt{3} sqrt{sin{left (x right )}} + 2 sin{left (x right )}$$
