tan(17*c*1/10)*tan(17/10)+(-cot(5*p^6))^2-6*sin(2*p)-6*cos(2*p) если p=4 (упростите выражение)

Дано

$$\tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \left(- \cot{\left (5 p^{6} \right )}\right)^{2} — 6 \sin{\left (2 p \right )} — 6 \cos{\left (2 p \right )}$$
Подстановка условия
$$\tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \left(-1 \cot{\left (5 p^{6} \right )}\right)^{2} + -1 \cdot 6 \sin{\left (2 p \right )} + -1 \cdot 6 \cos{\left (2 p \right )}$$

tan((17*c)/10)*tan(17/10) + (-cot(5*(4)^6))^2 — 6*sin(2*(4)) — 6*cos(2*(4))

$$\tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \left(-1 \cot{\left (5 (4)^{6} \right )}\right)^{2} + -1 \cdot 6 \sin{\left (2 (4) \right )} + -1 \cdot 6 \cos{\left (2 (4) \right )}$$

tan((17*c)/10)*tan(17/10) + (-cot(5*4^6))^2 — 6*sin(2*4) — 6*cos(2*4)

$$\tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \left(-1 \cot{\left (5 \cdot 4^{6} \right )}\right)^{2} + -1 \cdot 6 \sin{\left (2 \cdot 4 \right )} + -1 \cdot 6 \cos{\left (2 \cdot 4 \right )}$$

cot(20480)^2 — 6*cos(8) — 6*sin(8) + tan(17/10)*tan(17*c/10)

$$\tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} — 6 \sin{\left (8 \right )} — 6 \cos{\left (8 \right )} + \cot^{2}{\left (20480 \right )}$$
Читайте также  (x-6)=sqrt(8-x)
Степени
$$- 6 \sin{\left (2 p \right )} — 6 \cos{\left (2 p \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \cot^{2}{\left (5 p^{6} \right )}$$
Численный ответ

cot(5*p^6)^2 — 6.0*cos(2*p) — 6.0*sin(2*p) — 7.69660213945916*tan((17*c)/10)

Рациональный знаменатель
$$- 6 \sin{\left (2 p \right )} — 6 \cos{\left (2 p \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \cot^{2}{\left (5 p^{6} \right )}$$
Объединение рациональных выражений
$$- 6 \sin{\left (2 p \right )} — 6 \cos{\left (2 p \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \cot^{2}{\left (5 p^{6} \right )}$$
Общее упрощение

1 /17 /17*c ___ / pi
———- + tan|—|*tan|—-| — 6*/ 2 *sin|2*p + —|
2/ 6 10/ 10 / 4 /
tan 5*p /

$$- 6 \sqrt{2} \sin{\left (2 p + \frac{\pi}{4} \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \frac{1}{\tan^{2}{\left (5 p^{6} \right )}}$$
Соберем выражение
$$- 6 \sin{\left (2 p \right )} — 6 \cos{\left (2 p \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \left(- \cot{\left (5 p^{6} \right )}\right)^{2}$$
Читайте также  7200/x=800

2/ 6 /17 /17*c
cot 5*p / — 6*cos(2*p) — 6*sin(2*p) + tan|—|*tan|—-|
10/ 10 /

$$- 6 \sin{\left (2 p \right )} — 6 \cos{\left (2 p \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \cot^{2}{\left (5 p^{6} \right )}$$
Общий знаменатель

2/ 6 /17 /17*c
cot 5*p / — 6*cos(2*p) — 6*sin(2*p) + tan|—|*tan|—-|
10/ 10 /

$$- 6 \sin{\left (2 p \right )} — 6 \cos{\left (2 p \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \cot^{2}{\left (5 p^{6} \right )}$$
Тригонометрическая часть

1 /17 /17*c ___ / pi
———- + tan|—|*tan|—-| — 6*/ 2 *sin|2*p + —|
2/ 6 10/ 10 / 4 /
tan 5*p /

$$- 6 \sqrt{2} \sin{\left (2 p + \frac{\pi}{4} \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \frac{1}{\tan^{2}{\left (5 p^{6} \right )}}$$
Комбинаторика

2/ 6 /17 /17*c
cot 5*p / — 6*cos(2*p) — 6*sin(2*p) + tan|—|*tan|—-|
10/ 10 /

$$- 6 \sin{\left (2 p \right )} — 6 \cos{\left (2 p \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \cot^{2}{\left (5 p^{6} \right )}$$
Читайте также  cos(2*x)=-1/2
Раскрыть выражение

2
/ 5/ 6 3/ 6 / 6\
2 2 \cot p / — 10*cot p / + 5*cotp // /17 /17*c
— 6*cos (p) + 6*sin (p) + ————————————- + tan|—|*tan|—-| — 12*cos(p)*sin(p)
2 10/ 10 /
/ 2/ 6 4/ 6\
1 — 10*cot p / + 5*cot p //

$$6 \sin^{2}{\left (p \right )} — 12 \sin{\left (p \right )} \cos{\left (p \right )} — 6 \cos^{2}{\left (p \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \frac{\left(\cot^{5}{\left (p^{6} \right )} — 10 \cot^{3}{\left (p^{6} \right )} + 5 \cot{\left (p^{6} \right )}\right)^{2}}{\left(5 \cot^{4}{\left (p^{6} \right )} — 10 \cot^{2}{\left (p^{6} \right )} + 1\right)^{2}}$$

2/ 6 /17*c /17
cot 5*p / + tan|—-|*tan|—| — 6*cos(2*p) — 6*sin(2*p)
10 / 10/

$$- 6 \sin{\left (2 p \right )} — 6 \cos{\left (2 p \right )} + \tan{\left (\frac{17}{10} \right )} \tan{\left (\frac{17 c}{10} \right )} + \cot^{2}{\left (5 p^{6} \right )}$$
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