(sin(a)+sin(3*a)+sin(5*a)+sin(7*a))*1/(cos(a)+cos(3*a)+cos(5*a)+cos(7*a)) если a=-4 (упростите выражение)

$$frac{sin{left (a right )} + sin{left (3 a right )} + sin{left (5 a right )} + sin{left (7 a right )}}{cos{left (a right )} + cos{left (3 a right )} + cos{left (5 a right )} + cos{left (7 a right )}}$$

$$frac{sin{left (a right )} + sin{left (3 a right )} + sin{left (5 a right )} + sin{left (7 a right )}}{cos{left (a right )} + cos{left (3 a right )} + cos{left (5 a right )} + cos{left (7 a right )}}$$

(sin((-4)) + sin(3*(-4)) + sin(5*(-4)) + sin(7*(-4)))/(cos((-4)) + cos(3*(-4)) + cos(5*(-4)) + cos(7*(-4)))

$$frac{sin{left ((-4) right )} + sin{left (3 (-4) right )} + sin{left (5 (-4) right )} + sin{left (7 (-4) right )}}{cos{left ((-4) right )} + cos{left (3 (-4) right )} + cos{left (5 (-4) right )} + cos{left (7 (-4) right )}}$$

(sin(-4) + sin(3*(-4)) + sin(5*(-4)) + sin(7*(-4)))/(cos(-4) + cos(3*(-4)) + cos(5*(-4)) + cos(7*(-4)))

$$frac{sin{left (-4 cdot 7 right )} + sin{left (-4 cdot 5 right )} + sin{left (-4 cdot 3 right )} + sin{left (-4 right )}}{cos{left (-4 cdot 7 right )} + cos{left (-4 right )} + cos{left (-4 cdot 3 right )} + cos{left (-4 cdot 5 right )}}$$

(-sin(4) – sin(12) – sin(20) – sin(28))/(cos(4) + cos(12) + cos(20) + cos(28))

$$frac{- sin{left (20 right )} – sin{left (28 right )} – sin{left (12 right )} – sin{left (4 right )}}{cos{left (28 right )} + cos{left (4 right )} + cos{left (20 right )} + cos{left (12 right )}}$$

(sin(a) + sin(3*a) + sin(5*a) + sin(7*a))/(cos(a) + cos(3*a) + cos(5*a) + cos(7*a))

$$frac{sin{left (a right )}}{cos{left (a right )} + cos{left (3 a right )} + cos{left (5 a right )} + cos{left (7 a right )}} + frac{sin{left (3 a right )}}{cos{left (a right )} + cos{left (3 a right )} + cos{left (5 a right )} + cos{left (7 a right )}} + frac{sin{left (5 a right )}}{cos{left (a right )} + cos{left (3 a right )} + cos{left (5 a right )} + cos{left (7 a right )}} + frac{sin{left (7 a right )}}{cos{left (a right )} + cos{left (3 a right )} + cos{left (5 a right )} + cos{left (7 a right )}}$$

5 3 7 4 3 2 3 2 4 6 2 5
sin (a) – sin (a) – sin (a) – 35*cos (a)*sin (a) – 10*cos (a)*sin (a) + 3*cos (a)*sin(a) + 5*cos (a)*sin(a) + 7*cos (a)*sin(a) + 21*cos (a)*sin (a) + sin(a)
————————————————————————————————————————————————————
3 5 7 5 2 3 2 6 2 4 3 4
cos (a) + cos (a) + cos (a) – 21*cos (a)*sin (a) – 10*cos (a)*sin (a) – 7*sin (a)*cos(a) – 3*sin (a)*cos(a) + 5*sin (a)*cos(a) + 35*cos (a)*sin (a) + cos(a)

$$frac{- sin^{7}{left (a right )} + 21 sin^{5}{left (a right )} cos^{2}{left (a right )} + sin^{5}{left (a right )} – 35 sin^{3}{left (a right )} cos^{4}{left (a right )} – 10 sin^{3}{left (a right )} cos^{2}{left (a right )} – sin^{3}{left (a right )} + 7 sin{left (a right )} cos^{6}{left (a right )} + 5 sin{left (a right )} cos^{4}{left (a right )} + 3 sin{left (a right )} cos^{2}{left (a right )} + sin{left (a right )}}{- 7 sin^{6}{left (a right )} cos{left (a right )} + 35 sin^{4}{left (a right )} cos^{3}{left (a right )} + 5 sin^{4}{left (a right )} cos{left (a right )} – 21 sin^{2}{left (a right )} cos^{5}{left (a right )} – 10 sin^{2}{left (a right )} cos^{3}{left (a right )} – 3 sin^{2}{left (a right )} cos{left (a right )} + cos^{7}{left (a right )} + cos^{5}{left (a right )} + cos^{3}{left (a right )} + cos{left (a right )}}$$