(3+cos(4*x)-8*cos(x)^4)*1/(4*(cos(x)+sin(x))) если x=1/3 (упростите выражение)

$$frac{cos{left (4 x right )} + 3 – 8 cos^{4}{left (x right )}}{4 left(sin{left (x right )} + cos{left (x right )}right)}$$

$$frac{cos{left (4 x right )} + 3 – 8 cos^{4}{left (x right )}}{4 left(sin{left (x right )} + cos{left (x right )}right)}$$

(3 + cos(4*(1/3)) – 8*cos((1/3))^4)/(4*(cos((1/3)) + sin((1/3))))

$$frac{cos{left (4 (1/3) right )} + 3 – 8 cos^{4}{left ((1/3) right )}}{4 left(sin{left ((1/3) right )} + cos{left ((1/3) right )}right)}$$

(3 + cos(4/3) – 8*cos(1/3)^4)/(4*(cos(1/3) + sin(1/3)))

$$frac{- 8 cos^{4}{left (frac{1}{3} right )} + cos{left (frac{4}{3} right )} + 3}{4 left(sin{left (frac{1}{3} right )} + cos{left (frac{1}{3} right )}right)}$$

(3 – 8*cos(1/3)^4 + cos(4/3))/(4*cos(1/3) + 4*sin(1/3))

$$frac{- 8 cos^{4}{left (frac{1}{3} right )} + cos{left (frac{4}{3} right )} + 3}{4 sin{left (frac{1}{3} right )} + 4 cos{left (frac{1}{3} right )}}$$

$$frac{- 8 cos^{4}{left (x right )} + cos{left (4 x right )} + 3}{4 sin{left (x right )} + 4 cos{left (x right )}}$$

(3.0 – 8.0*cos(x)^4 + cos(4*x))/(4.0*cos(x) + 4.0*sin(x))

$$frac{- 8 cos^{4}{left (x right )} + cos{left (4 x right )} + 3}{4 sin{left (x right )} + 4 cos{left (x right )}}$$

$$frac{- 8 cos^{4}{left (x right )} + cos{left (4 x right )} + 3}{4 sin{left (x right )} + 4 cos{left (x right )}}$$

___
-/ 2 *cos(2*x)
—————-
/ pi
2*sin|x + –|
4 /

$$- frac{sqrt{2} cos{left (2 x right )}}{2 sin{left (x + frac{pi}{4} right )}}$$

$$frac{- 8 cos^{4}{left (x right )} + cos{left (4 x right )} + 3}{4 sin{left (x right )} + 4 cos{left (x right )}}$$

-cos(2*x)
—————
cos(x) + sin(x)

$$- frac{cos{left (2 x right )}}{sin{left (x right )} + cos{left (x right )}}$$

4
3 3 3 – 8*sin (x) + cos(4*x) 2 2
– 2*cos (x) + 2*sin (x) + ———————— – 2*sin (x)*cos(x) + 2*cos (x)*sin(x)
4*cos(x) + 4*sin(x)

$$2 sin^{3}{left (x right )} – 2 sin^{2}{left (x right )} cos{left (x right )} + 2 sin{left (x right )} cos^{2}{left (x right )} – 2 cos^{3}{left (x right )} + frac{- 8 sin^{4}{left (x right )} + cos{left (4 x right )} + 3}{4 sin{left (x right )} + 4 cos{left (x right )}}$$

___
-/ 2 *cos(2*x)
—————-
/ pi
2*sin|x + –|
4 /

$$- frac{sqrt{2} cos{left (2 x right )}}{2 sin{left (x + frac{pi}{4} right )}}$$

4
3 – 8*cos (x) + cos(4*x)
————————
4*(cos(x) + sin(x))

$$frac{- 8 cos^{4}{left (x right )} + cos{left (4 x right )} + 3}{4 sin{left (x right )} + 4 cos{left (x right )}}$$

4
3 + cos(4*x) – 8*cos (x)
————————
4*(cos(x) + sin(x))

$$frac{cos{left (4 x right )} + 3 – 8 cos^{4}{left (x right )}}{4 sin{left (x right )} + 4 cos{left (x right )}}$$

4 4 2 2
3 + sin (x) – 7*cos (x) – 6*cos (x)*sin (x)
——————————————-
4*cos(x) + 4*sin(x)

$$frac{sin^{4}{left (x right )} – 6 sin^{2}{left (x right )} cos^{2}{left (x right )} – 7 cos^{4}{left (x right )} + 3}{4 sin{left (x right )} + 4 cos{left (x right )}}$$