sin(40)-2*cos(sin(x)^2*15)^10+sin(20) если x=-4 (упростите выражение)

Вы ввели

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sin(40) - 2*cos  \sin (x)*15/ + sin(20)

$$- 2 \cos^{10}{\left (15 \sin^{2}{\left (x \right )} \right )} + \sin{\left (40 \right )} + \sin{\left (20 \right )}$$

Подстановка условия

sin(40) - 2*cos(sin(x)^2*15)^10 + sin(20) при x = -4

sin(40) - 2*cos(sin(x)^2*15)^10 + sin(20)

$$- 2 \cos^{10}{\left (15 \sin^{2}{\left (x \right )} \right )} + \sin{\left (40 \right )} + \sin{\left (20 \right )}$$

sin(40) - 2*cos(sin((-4))^2*15)^10 + sin(20)

$$- 2 \cos^{10}{\left (15 \sin^{2}{\left ((-4) \right )} \right )} + \sin{\left (40 \right )} + \sin{\left (20 \right )}$$

sin(40) - 2*cos(sin(-4)^2*15)^10 + sin(20)

$$- 2 \cos^{10}{\left (15 \sin^{2}{\left (-4 \right )} \right )} + \sin{\left (40 \right )} + \sin{\left (20 \right )}$$

-2*cos(15*sin(4)^2)^10 + sin(20) + sin(40)

$$- 2 \cos^{10}{\left (15 \sin^{2}{\left (4 \right )} \right )} + \sin{\left (40 \right )} + \sin{\left (20 \right )}$$

Численный ответ

1.65805841120698 - 2.0*cos(sin(x)^2*15)^10

Собрать выражение

   63   105*cos(-15 + 15*cos(2*x))   45*cos(-45 + 45*cos(2*x))   15*cos(-30 + 30*cos(2*x))   5*cos(-60 + 60*cos(2*x))   cos(-75 + 75*cos(2*x))                    
- --- - -------------------------- - ------------------------- - ------------------------- - ------------------------ - ---------------------- + sin(20) + sin(40)
  128              128                          256                          32                        128                       256                              

$$- \frac{105}{128} \cos{\left (15 \cos{\left (2 x \right )} - 15 \right )} - \frac{15}{32} \cos{\left (30 \cos{\left (2 x \right )} - 30 \right )} - \frac{45}{256} \cos{\left (45 \cos{\left (2 x \right )} - 45 \right )} - \frac{5}{128} \cos{\left (60 \cos{\left (2 x \right )} - 60 \right )} - \frac{1}{256} \cos{\left (75 \cos{\left (2 x \right )} - 75 \right )} - \frac{63}{128} + \sin{\left (40 \right )} + \sin{\left (20 \right )}$$

Раскрыть выражение

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    /   15/   2   \           9/   2   \    6/   2   \           5/   2   \    10/   2   \          13/   2   \    2/   2   \         14/   2   \    /   2   \          3/   2   \    12/   2   \           11/   2   \    4/   2   \           7/   2   \    8/   2   \\                      
- 2*\cos  \sin (x)/ - 5005*cos \sin (x)/*sin \sin (x)/ - 3003*cos \sin (x)/*sin  \sin (x)/ - 105*cos  \sin (x)/*sin \sin (x)/ - 15*sin  \sin (x)/*cos\sin (x)/ + 455*cos \sin (x)/*sin  \sin (x)/ + 1365*cos  \sin (x)/*sin \sin (x)/ + 6435*cos \sin (x)/*sin \sin (x)//   + sin(20) + sin(40)

$$- 2 \left(- 15 \sin^{14}{\left (\sin^{2}{\left (x \right )} \right )} \cos{\left (\sin^{2}{\left (x \right )} \right )} + 455 \sin^{12}{\left (\sin^{2}{\left (x \right )} \right )} \cos^{3}{\left (\sin^{2}{\left (x \right )} \right )} - 3003 \sin^{10}{\left (\sin^{2}{\left (x \right )} \right )} \cos^{5}{\left (\sin^{2}{\left (x \right )} \right )} + 6435 \sin^{8}{\left (\sin^{2}{\left (x \right )} \right )} \cos^{7}{\left (\sin^{2}{\left (x \right )} \right )} - 5005 \sin^{6}{\left (\sin^{2}{\left (x \right )} \right )} \cos^{9}{\left (\sin^{2}{\left (x \right )} \right )} + 1365 \sin^{4}{\left (\sin^{2}{\left (x \right )} \right )} \cos^{11}{\left (\sin^{2}{\left (x \right )} \right )} - 105 \sin^{2}{\left (\sin^{2}{\left (x \right )} \right )} \cos^{13}{\left (\sin^{2}{\left (x \right )} \right )} + \cos^{15}{\left (\sin^{2}{\left (x \right )} \right )}\right)^{10} + \sin{\left (40 \right )} + \sin{\left (20 \right )}$$