(-log(sin(x)^2-1))*1/2+log(sin(x))-(6*sin(x)^4-15*sin(x)^2+11)*1/(-12+36*sin(x)^2-36*sin(x)^4+12*sin(x)^6) если x=4 (упростите выражение)

$$frac{1}{2} left(-1 log{left (sin^{2}{left (x right )} – 1 right )}right) + log{left (sin{left (x right )} right )} – frac{6 sin^{4}{left (x right )} – 15 sin^{2}{left (x right )} + 11}{36 sin^{2}{left (x right )} – 12 – 36 sin^{4}{left (x right )} + 12 sin^{6}{left (x right )}}$$

$$frac{1}{2} left(-1 log{left (sin^{2}{left (x right )} – 1 right )}right) + log{left (sin{left (x right )} right )} – frac{6 sin^{4}{left (x right )} – 15 sin^{2}{left (x right )} + 11}{36 sin^{2}{left (x right )} – 12 – 36 sin^{4}{left (x right )} + 12 sin^{6}{left (x right )}}$$

(-log(sin((4))^2 – 1))/2 + log(sin((4))) – (6*sin((4))^4 – 15*sin((4))^2 + 11)/(-12 + 36*sin((4))^2 – 36*sin((4))^4 + 12*sin((4))^6)

$$frac{1}{2} left(-1 log{left (sin^{2}{left ((4) right )} – 1 right )}right) + log{left (sin{left ((4) right )} right )} – frac{6 sin^{4}{left ((4) right )} – 15 sin^{2}{left ((4) right )} + 11}{36 sin^{2}{left ((4) right )} – 12 – 36 sin^{4}{left ((4) right )} + 12 sin^{6}{left ((4) right )}}$$

(-log(sin(4)^2 – 1))/2 + log(sin(4)) – (6*sin(4)^4 – 15*sin(4)^2 + 11)/(-12 + 36*sin(4)^2 – 36*sin(4)^4 + 12*sin(4)^6)

$$- frac{- 15 sin^{2}{left (4 right )} + 6 sin^{4}{left (4 right )} + 11}{- 36 sin^{4}{left (4 right )} + -12 + 36 sin^{2}{left (4 right )} + 12 sin^{6}{left (4 right )}} + frac{1}{2} left(-1 log{left (-1 + sin^{2}{left (4 right )} right )}right) + log{left (sin{left (4 right )} right )}$$

-log(1 – sin(4)^2)/2 + pi*i/2 – (11 – 15*sin(4)^2 + 6*sin(4)^4)/(-12 – 36*sin(4)^4 + 12*sin(4)^6 + 36*sin(4)^2) + log(-sin(4))

$$log{left (- sin{left (4 right )} right )} – frac{1}{2} log{left (- sin^{2}{left (4 right )} + 1 right )} – frac{- 15 sin^{2}{left (4 right )} + 6 sin^{4}{left (4 right )} + 11}{-12 – 36 sin^{4}{left (4 right )} + 12 sin^{6}{left (4 right )} + 36 sin^{2}{left (4 right )}} + frac{i pi}{2}$$

$$frac{- 6 sin^{4}{left (x right )} + 15 sin^{2}{left (x right )} – 11}{12 sin^{6}{left (x right )} – 36 sin^{4}{left (x right )} + 36 sin^{2}{left (x right )} – 12} – frac{1}{2} log{left (sin^{2}{left (x right )} – 1 right )} + log{left (sin{left (x right )} right )}$$

/ 2 2 4
log -1 + sin (x)/ 11 – 15*sin (x) + 6*sin (x)
– —————– – —————————————— + log(sin(x))
2 4 6 2
-12 – 36*sin (x) + 12*sin (x) + 36*sin (x)

$$- frac{6 sin^{4}{left (x right )} – 15 sin^{2}{left (x right )} + 11}{12 sin^{6}{left (x right )} – 36 sin^{4}{left (x right )} + 36 sin^{2}{left (x right )} – 12} – frac{1}{2} log{left (sin^{2}{left (x right )} – 1 right )} + log{left (sin{left (x right )} right )}$$

-0.5*log(sin(x)^2 – 1) – (11.0 + 6.0*sin(x)^4 – 15.0*sin(x)^2)/(-12.0 + 12.0*sin(x)^6 + 36.0*sin(x)^2 – 36.0*sin(x)^4) + log(sin(x))

$$frac{1}{12 sin^{6}{left (x right )} – 36 sin^{4}{left (x right )} + 36 sin^{2}{left (x right )} – 12} left(- 6 log{left (sin^{2}{left (x right )} – 1 right )} sin^{6}{left (x right )} + 18 log{left (sin^{2}{left (x right )} – 1 right )} sin^{4}{left (x right )} – 18 log{left (sin^{2}{left (x right )} – 1 right )} sin^{2}{left (x right )} + 6 log{left (sin^{2}{left (x right )} – 1 right )} + 12 log{left (sin{left (x right )} right )} sin^{6}{left (x right )} – 36 log{left (sin{left (x right )} right )} sin^{4}{left (x right )} + 36 log{left (sin{left (x right )} right )} sin^{2}{left (x right )} – 12 log{left (sin{left (x right )} right )} – 6 sin^{4}{left (x right )} + 15 sin^{2}{left (x right )} – 11right)$$

$$frac{1}{12 sin^{6}{left (x right )} – 36 sin^{4}{left (x right )} + 36 sin^{2}{left (x right )} – 12} left(6 left(- log{left (sin^{2}{left (x right )} – 1 right )} + 2 log{left (sin{left (x right )} right )}right) left(sin^{6}{left (x right )} – 3 sin^{4}{left (x right )} + 3 sin^{2}{left (x right )} – 1right) – 3 left(2 sin^{2}{left (x right )} – 5right) sin^{2}{left (x right )} – 11right)$$

/ 2 4
log -1 + sin (x)/ 1 5 sin (x)
– —————– – ——— + ——— + ——— + log(sin(x))
2 6 4 6
3*cos (x) 4*cos (x) 2*cos (x)

$$- frac{1}{2} log{left (sin^{2}{left (x right )} – 1 right )} + log{left (sin{left (x right )} right )} + frac{sin^{4}{left (x right )}}{2 cos^{6}{left (x right )}} + frac{5}{4 cos^{4}{left (x right )}} – frac{1}{3 cos^{6}{left (x right )}}$$

$$frac{- 6 sin^{4}{left (x right )} + 15 sin^{2}{left (x right )} – 11}{12 sin^{6}{left (x right )} – 36 sin^{4}{left (x right )} + 36 sin^{2}{left (x right )} – 12} – frac{1}{2} log{left (sin^{2}{left (x right )} – 1 right )} + log{left (sin{left (x right )} right )}$$

/ 1 cos(2*x)
log|- – – ——–|
46 2 2 / 2*cos(4*x) 12*cos(2*x)
——————————————- – ——————- + —————————————- + —————————————- + log(sin(x))
30 + 3*cos(6*x) + 18*cos(4*x) + 45*cos(2*x) 2 10 + 6*cos(4*x) + 15*cos(2*x) + cos(6*x) 10 + 6*cos(4*x) + 15*cos(2*x) + cos(6*x)

$$- frac{1}{2} log{left (- frac{1}{2} cos{left (2 x right )} – frac{1}{2} right )} + log{left (sin{left (x right )} right )} + frac{46}{45 cos{left (2 x right )} + 18 cos{left (4 x right )} + 3 cos{left (6 x right )} + 30} + frac{12 cos{left (2 x right )}}{15 cos{left (2 x right )} + 6 cos{left (4 x right )} + cos{left (6 x right )} + 10} + frac{2 cos{left (4 x right )}}{15 cos{left (2 x right )} + 6 cos{left (4 x right )} + cos{left (6 x right )} + 10}$$

/ 2 2 4
log -1 + sin (x)/ 11 – 15*sin (x) + 6*sin (x)
– —————– – —————————————— + log(sin(x))
2 4 6 2
-12 – 36*sin (x) + 12*sin (x) + 36*sin (x)

$$- frac{6 sin^{4}{left (x right )} – 15 sin^{2}{left (x right )} + 11}{12 sin^{6}{left (x right )} – 36 sin^{4}{left (x right )} + 36 sin^{2}{left (x right )} – 12} – frac{1}{2} log{left (sin^{2}{left (x right )} – 1 right )} + log{left (sin{left (x right )} right )}$$

/ 2 2 4
log -cos (x)/ 11 – 15*sin (x) + 6*sin (x)
– ————- + ————————— + log(sin(x))
2 6
12*cos (x)

$$frac{1}{12 cos^{6}{left (x right )}} left(6 sin^{4}{left (x right )} – 15 sin^{2}{left (x right )} + 11right) + log{left (sin{left (x right )} right )} – frac{1}{2} log{left (- cos^{2}{left (x right )} right )}$$

4 / 2 2 4 2 / 2 6 / 2 6 4 / 2 2
-11 – 12*log(sin(x)) – 6*sin (x) + 6*log -1 + sin (x)/ + 15*sin (x) – 36*sin (x)*log(sin(x)) – 18*sin (x)*log -1 + sin (x)/ – 6*sin (x)*log -1 + sin (x)/ + 12*sin (x)*log(sin(x)) + 18*sin (x)*log -1 + sin (x)/ + 36*sin (x)*log(sin(x))
——————————————————————————————————————————————————————————————————————————————
3 3
12*(1 + sin(x)) *(-1 + sin(x))

$$frac{1}{12 left(sin{left (x right )} – 1right)^{3} left(sin{left (x right )} + 1right)^{3}} left(- 6 log{left (sin^{2}{left (x right )} – 1 right )} sin^{6}{left (x right )} + 18 log{left (sin^{2}{left (x right )} – 1 right )} sin^{4}{left (x right )} – 18 log{left (sin^{2}{left (x right )} – 1 right )} sin^{2}{left (x right )} + 6 log{left (sin^{2}{left (x right )} – 1 right )} + 12 log{left (sin{left (x right )} right )} sin^{6}{left (x right )} – 36 log{left (sin{left (x right )} right )} sin^{4}{left (x right )} + 36 log{left (sin{left (x right )} right )} sin^{2}{left (x right )} – 12 log{left (sin{left (x right )} right )} – 6 sin^{4}{left (x right )} + 15 sin^{2}{left (x right )} – 11right)$$

/ 2 4 2
log -1 + sin (x)/ -11 – 6*sin (x) + 15*sin (x)
– —————– + —————————————— + log(sin(x))
2 4 6 2
-12 – 36*sin (x) + 12*sin (x) + 36*sin (x)

$$frac{- 6 sin^{4}{left (x right )} + 15 sin^{2}{left (x right )} – 11}{12 sin^{6}{left (x right )} – 36 sin^{4}{left (x right )} + 36 sin^{2}{left (x right )} – 12} – frac{1}{2} log{left (sin^{2}{left (x right )} – 1 right )} + log{left (sin{left (x right )} right )}$$