Дано
$$frac{1}{7} cos{left (2 p right )} + frac{1}{7} cos{left (4 p right )} + frac{1}{7} cos{left (6 p right )}$$
Подстановка условия
$$frac{1}{7} cos{left (2 p right )} + frac{1}{7} cos{left (4 p right )} + frac{1}{7} cos{left (6 p right )}$$
cos(2*(1/2))/7 + cos(4*(1/2))/7 + cos(6*(1/2))/7
$$frac{1}{7} cos{left (2 (1/2) right )} + frac{1}{7} cos{left (4 (1/2) right )} + frac{1}{7} cos{left (6 (1/2) right )}$$
cos(2/2)/7 + cos(4/2)/7 + cos(6/2)/7
$$frac{1}{7} cos{left (frac{6}{2} right )} + frac{1}{7} cos{left (frac{4}{2} right )} + frac{1}{7} cos{left (frac{2}{2} right )}$$
cos(1)/7 + cos(2)/7 + cos(3)/7
$$frac{1}{7} cos{left (3 right )} + frac{1}{7} cos{left (2 right )} + frac{1}{7} cos{left (1 right )}$$
Численный ответ
0.142857142857143*cos(2*p) + 0.142857142857143*cos(4*p) + 0.142857142857143*cos(6*p)
Объединение рациональных выражений
$$frac{1}{7} left(cos{left (2 p right )} + cos{left (4 p right )} + cos{left (6 p right )}right)$$
Тригонометрическая часть
cos(2*p) + cos(4*p) cos(6*p)
——————- + ——–
7 7
$$frac{1}{7} left(cos{left (2 p right )} + cos{left (4 p right )}right) + frac{1}{7} cos{left (6 p right )}$$
Комбинаторика
cos(2*p) + cos(4*p) + cos(6*p)
——————————
7
$$frac{1}{7} left(cos{left (2 p right )} + cos{left (4 p right )} + cos{left (6 p right )}right)$$
Раскрыть выражение
2 6 2 4 6 4 4 2 2 2 2 4
sin (p) sin (p) cos (p) cos (p) cos (p) sin (p) 15*cos (p)*sin (p) 6*cos (p)*sin (p) 15*cos (p)*sin (p)
– ——- – ——- + ——- + ——- + ——- + ——- – —————— – —————– + ——————
7 7 7 7 7 7 7 7 7
$$- frac{1}{7} sin^{6}{left (p right )} + frac{15}{7} sin^{4}{left (p right )} cos^{2}{left (p right )} + frac{1}{7} sin^{4}{left (p right )} – frac{15}{7} sin^{2}{left (p right )} cos^{4}{left (p right )} – frac{6}{7} sin^{2}{left (p right )} cos^{2}{left (p right )} – frac{1}{7} sin^{2}{left (p right )} + frac{1}{7} cos^{6}{left (p right )} + frac{1}{7} cos^{4}{left (p right )} + frac{1}{7} cos^{2}{left (p right )}$$
