sin(2*x)-sin(4*x)*1/cos(x)+cos(5*x)*(1+cos(4*x)) если x=1 (упростите выражение)

Дано

$$\sin{\left (2 x \right )} — \frac{\sin{\left (4 x \right )}}{\cos{\left (x \right )}} + \left(\cos{\left (4 x \right )} + 1\right) \cos{\left (5 x \right )}$$
Подстановка условия
$$\sin{\left (2 x \right )} — \frac{\sin{\left (4 x \right )}}{\cos{\left (x \right )}} + \left(\cos{\left (4 x \right )} + 1\right) \cos{\left (5 x \right )}$$

sin(2*(1)) — sin(4*(1))/cos((1)) + cos(5*(1))*(1 + cos(4*(1)))

$$\sin{\left (2 (1) \right )} — \frac{\sin{\left (4 (1) \right )}}{\cos{\left ((1) \right )}} + \left(\cos{\left (4 (1) \right )} + 1\right) \cos{\left (5 (1) \right )}$$

sin(2) — sin(4)/cos(1) + cos(5)*(1 + cos(4))

$$\left(\cos{\left (4 \right )} + 1\right) \cos{\left (5 \right )} + \sin{\left (2 \right )} — \frac{\sin{\left (4 \right )}}{\cos{\left (1 \right )}}$$

(1 + cos(4))*cos(5) — sin(4)/cos(1) + sin(2)

$$\left(\cos{\left (4 \right )} + 1\right) \cos{\left (5 \right )} + \sin{\left (2 \right )} — \frac{\sin{\left (4 \right )}}{\cos{\left (1 \right )}}$$
Степени
$$\left(\cos{\left (4 x \right )} + 1\right) \cos{\left (5 x \right )} + \sin{\left (2 x \right )} — \frac{\sin{\left (4 x \right )}}{\cos{\left (x \right )}}$$
Читайте также  (sqrt((1+sin(a))*1/(1-sin(a)))-sqrt((1-sin(a))*1/(1+sin(a))))*cot(a) если a=-1/3 (упростите выражение)
Численный ответ

(1.0 + cos(4*x))*cos(5*x) — sin(4*x)/cos(x) + sin(2*x)

Рациональный знаменатель
$$\frac{1}{\cos{\left (x \right )}} \left(\left(\cos{\left (4 x \right )} + 1\right) \cos{\left (x \right )} \cos{\left (5 x \right )} + \sin{\left (2 x \right )} \cos{\left (x \right )} — \sin{\left (4 x \right )}\right)$$
Объединение рациональных выражений
$$\frac{1}{\cos{\left (x \right )}} \left(\left(\cos{\left (4 x \right )} + 1\right) \cos{\left (x \right )} \cos{\left (5 x \right )} + \sin{\left (2 x \right )} \cos{\left (x \right )} — \sin{\left (4 x \right )}\right)$$
Общее упрощение

-sin(4*x) + ((1 + cos(4*x))*cos(5*x) + sin(2*x))*cos(x)
——————————————————-
cos(x)

$$\frac{1}{\cos{\left (x \right )}} \left(\left(\left(\cos{\left (4 x \right )} + 1\right) \cos{\left (5 x \right )} + \sin{\left (2 x \right )}\right) \cos{\left (x \right )} — \sin{\left (4 x \right )}\right)$$
Соберем выражение
$$\left(\cos{\left (4 x \right )} + 1\right) \cos{\left (5 x \right )} + \sin{\left (2 x \right )} — \frac{\sin{\left (4 x \right )}}{\cos{\left (x \right )}}$$
Читайте также  6*(x+11)=0

cos(x) cos(9*x)
—— + ——— — sec(x)*sin(4*x) + cos(5*x) + sin(2*x)
2 2

$$\sin{\left (2 x \right )} — \sin{\left (4 x \right )} sec{\left (x \right )} + \frac{1}{2} \cos{\left (x \right )} + \cos{\left (5 x \right )} + \frac{1}{2} \cos{\left (9 x \right )}$$
Общий знаменатель

sin(4*x)
cos(4*x)*cos(5*x) — ——— + cos(5*x) + sin(2*x)
cos(x)

$$\sin{\left (2 x \right )} — \frac{\sin{\left (4 x \right )}}{\cos{\left (x \right )}} + \cos{\left (4 x \right )} \cos{\left (5 x \right )} + \cos{\left (5 x \right )}$$
Тригонометрическая часть

sin(4*x)
(1 + cos(4*x))*cos(5*x) — ——— + sin(2*x)
cos(x)

$$\left(\cos{\left (4 x \right )} + 1\right) \cos{\left (5 x \right )} + \sin{\left (2 x \right )} — \frac{\sin{\left (4 x \right )}}{\cos{\left (x \right )}}$$
Комбинаторика

-sin(4*x) + cos(x)*cos(5*x) + cos(x)*sin(2*x) + cos(x)*cos(4*x)*cos(5*x)
————————————————————————
cos(x)

$$\frac{1}{\cos{\left (x \right )}} \left(\sin{\left (2 x \right )} \cos{\left (x \right )} — \sin{\left (4 x \right )} + \cos{\left (x \right )} \cos{\left (4 x \right )} \cos{\left (5 x \right )} + \cos{\left (x \right )} \cos{\left (5 x \right )}\right)$$
Читайте также  x^3=2
Раскрыть выражение

3 3
/ 5 3 2 4 / 4 4 2 2 — 4*sin (x)*cos(x) + 4*cos (x)*sin(x)
\cos (x) — 10*cos (x)*sin (x) + 5*sin (x)*cos(x)/*1 + cos (x) + sin (x) — 6*cos (x)*sin (x)/ — ————————————- + 2*cos(x)*sin(x)
cos(x)

$$- \frac{1}{\cos{\left (x \right )}} \left(- 4 \sin^{3}{\left (x \right )} \cos{\left (x \right )} + 4 \sin{\left (x \right )} \cos^{3}{\left (x \right )}\right) + \left(5 \sin^{4}{\left (x \right )} \cos{\left (x \right )} — 10 \sin^{2}{\left (x \right )} \cos^{3}{\left (x \right )} + \cos^{5}{\left (x \right )}\right) \left(\sin^{4}{\left (x \right )} — 6 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )} + 1\right) + 2 \sin{\left (x \right )} \cos{\left (x \right )}$$
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