(1+cos(a)^2+cos(a)^4)*1/(3*cos(a)^2+sin(a)^4) если a=-1/2 (упростите выражение)

$$frac{cos^{2}{left (a right )} + 1 + cos^{4}{left (a right )}}{sin^{4}{left (a right )} + 3 cos^{2}{left (a right )}}$$

$$frac{cos^{2}{left (a right )} + 1 + cos^{4}{left (a right )}}{sin^{4}{left (a right )} + 3 cos^{2}{left (a right )}}$$

(1 + cos((-1/2))^2 + cos((-1/2))^4)/(3*cos((-1/2))^2 + sin((-1/2))^4)

$$frac{cos^{2}{left ((-1/2) right )} + 1 + cos^{4}{left ((-1/2) right )}}{sin^{4}{left ((-1/2) right )} + 3 cos^{2}{left ((-1/2) right )}}$$

(1 + cos(-1/2)^2 + cos(-1/2)^4)/(3*cos(-1/2)^2 + sin(-1/2)^4)

$$frac{cos^{4}{left (- frac{1}{2} right )} + cos^{2}{left (- frac{1}{2} right )} + 1}{sin^{4}{left (- frac{1}{2} right )} + 3 cos^{2}{left (- frac{1}{2} right )}}$$

(1 + cos(1/2)^2 + cos(1/2)^4)/(sin(1/2)^4 + 3*cos(1/2)^2)

$$frac{cos^{4}{left (frac{1}{2} right )} + cos^{2}{left (frac{1}{2} right )} + 1}{sin^{4}{left (frac{1}{2} right )} + 3 cos^{2}{left (frac{1}{2} right )}}$$

$$frac{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}{sin^{4}{left (a right )} + 3 cos^{2}{left (a right )}}$$

(1.0 + cos(a)^2 + cos(a)^4)/(sin(a)^4 + 3.0*cos(a)^2)

$$frac{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}{sin^{4}{left (a right )} + 3 cos^{2}{left (a right )}}$$

$$frac{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}{sin^{4}{left (a right )} + 3 cos^{2}{left (a right )}}$$

2 4
1 + cos (a) + cos (a)
———————
4 2
sin (a) + 3*cos (a)

$$frac{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}{sin^{4}{left (a right )} + 3 cos^{2}{left (a right )}}$$

$$frac{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}{sin^{4}{left (a right )} + 3 cos^{2}{left (a right )}}$$

1

$$1$$

/ 2 / 2
1 + cos (a) – cos(a)/*1 + cos (a) + cos(a)/
———————————————
4 2
sin (a) + 3*cos (a)

$$frac{1}{sin^{4}{left (a right )} + 3 cos^{2}{left (a right )}} left(cos^{2}{left (a right )} – cos{left (a right )} + 1right) left(cos^{2}{left (a right )} + cos{left (a right )} + 1right)$$

4 2 8 4
1 sin (a) cos (a) 9 + sin (a) – 3*sin (a)
– – ——- + ——- + ———————–
3 9 3 4 2
9*sin (a) + 27*cos (a)

$$- frac{1}{9} sin^{4}{left (a right )} + frac{1}{3} cos^{2}{left (a right )} + frac{1}{3} + frac{sin^{8}{left (a right )} – 3 sin^{4}{left (a right )} + 9}{9 sin^{4}{left (a right )} + 27 cos^{2}{left (a right )}}$$

2 4
1 + cos (a) + cos (a)
———————
4 2
sin (a) + 3*cos (a)

$$frac{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}{sin^{4}{left (a right )} + 3 cos^{2}{left (a right )}}$$