Дано
$$sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} + tan{left (frac{2 p}{4} right )} – sin^{2}{left (frac{2 p}{3} right )}$$
Подстановка условия
$$sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} + tan{left (frac{2 p}{4} right )} – sin^{2}{left (frac{2 p}{3} right )}$$
tan((2*(-4))/4) + cos((5*(-4))/3)*sin((7*(-4))/6) – sin((2*(-4))/3)^2
$$sin{left (frac{7 (-4)}{6} right )} cos{left (frac{5 (-4)}{3} right )} + tan{left (frac{2 (-4)}{4} right )} – sin^{2}{left (frac{2 (-4)}{3} right )}$$
tan((2*(-4))/4) + cos((5*(-4))/3)*sin((7*(-4))/6) – sin((2*(-4))/3)^2
$$- sin^{2}{left (frac{-8}{3} 1 right )} + sin{left (frac{-28}{6} 1 right )} cos{left (frac{-20}{3} 1 right )} + tan{left (frac{-8}{4} 1 right )}$$
-sin(8/3)^2 – tan(2) – cos(20/3)*sin(14/3)
$$- sin^{2}{left (frac{8}{3} right )} – sin{left (frac{14}{3} right )} cos{left (frac{20}{3} right )} – tan{left (2 right )}$$
Степени
$$- sin^{2}{left (frac{2 p}{3} right )} + sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} + tan{left (frac{p}{2} right )}$$
Численный ответ
-sin((2*p)/3)^2 + cos((5*p)/3)*sin((7*p)/6) + tan((2*p)/4)
Рациональный знаменатель
$$- sin^{2}{left (frac{2 p}{3} right )} + sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} + tan{left (frac{p}{2} right )}$$
Объединение рациональных выражений
$$- sin^{2}{left (frac{2 p}{3} right )} + sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} + tan{left (frac{p}{2} right )}$$
Общее упрощение
2/2*p /5*p /7*p /p
– sin |—| + cos|—|*sin|—| + tan|-|
3 / 3 / 6 / 2/
$$- sin^{2}{left (frac{2 p}{3} right )} + sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} + tan{left (frac{p}{2} right )}$$
Соберем выражение
$$- frac{1}{2} sin{left (frac{p}{2} right )} + frac{1}{2} sin{left (frac{17 p}{6} right )} + frac{1}{2} cos{left (frac{4 p}{3} right )} + tan{left (frac{p}{2} right )} – frac{1}{2}$$
2/2*p /5*p /7*p /2*p
– sin |—| + cos|—|*sin|—| + tan|—|
3 / 3 / 6 / 4 /
$$sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} – sin^{2}{left (frac{2 p}{3} right )} + tan{left (frac{2 p}{4} right )}$$
Общий знаменатель
2/2*p /5*p /7*p /p
– sin |—| + cos|—|*sin|—| + tan|-|
3 / 3 / 6 / 2/
$$- sin^{2}{left (frac{2 p}{3} right )} + sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} + tan{left (frac{p}{2} right )}$$
Тригонометрическая часть
2/2*p /5*p /7*p /p
– sin |—| + cos|—|*sin|—| + tan|-|
3 / 3 / 6 / 2/
$$- sin^{2}{left (frac{2 p}{3} right )} + sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} + tan{left (frac{p}{2} right )}$$
Комбинаторика
2/2*p /5*p /7*p /p
– sin |—| + cos|—|*sin|—| + tan|-|
3 / 3 / 6 / 2/
$$- sin^{2}{left (frac{2 p}{3} right )} + sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} + tan{left (frac{p}{2} right )}$$
Раскрыть выражение
2/2*p /5*p /7*p /p
– sin |—| + cos|—|*sin|—| + tan|-|
3 / 3 / 6 / 2/
$$- sin^{2}{left (frac{2 p}{3} right )} + sin{left (frac{7 p}{6} right )} cos{left (frac{5 p}{3} right )} + tan{left (frac{p}{2} right )}$$
