sin(30*x)*cos(30*x) если x=4 (упростите выражение)

Вы ввели

sin(30*x)*cos(30*x)

$$\sin{\left (30 x \right )} \cos{\left (30 x \right )}$$

Подстановка условия

sin(30*x)*cos(30*x) при x = 4

sin(30*x)*cos(30*x)

$$\sin{\left (30 x \right )} \cos{\left (30 x \right )}$$

sin(30*(4))*cos(30*(4))

$$\sin{\left (30 (4) \right )} \cos{\left (30 (4) \right )}$$

sin(30*4)*cos(30*4)

$$\sin{\left (4 \cdot 30 \right )} \cos{\left (4 \cdot 30 \right )}$$

cos(120)*sin(120)

$$\sin{\left (120 \right )} \cos{\left (120 \right )}$$

Численный ответ

cos(30*x)*sin(30*x)

Общее упрощение

sin(60*x)
---------
    2    

$$\frac{1}{2} \sin{\left (60 x \right )}$$

Собрать выражение

sin(60*x)
---------
    2    

$$\frac{1}{2} \sin{\left (60 x \right )}$$

Тригонометрическая часть

sin(60*x)
---------
    2    

$$\frac{1}{2} \sin{\left (60 x \right )}$$

Раскрыть выражение

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\- 155117520*cos  (x)*sin  (x) - 54627300*cos  (x)*sin  (x) - 54627300*cos  (x)*sin  (x) - 2035800*cos (x)*sin  (x) - 2035800*cos  (x)*sin (x) - 4060*cos (x)*sin  (x) - 4060*cos  (x)*sin (x) + 30*cos  (x)*sin(x) + 30*sin  (x)*cos(x) + 142506*cos (x)*sin  (x) + 142506*cos  (x)*sin (x) + 14307150*cos (x)*sin  (x) + 14307150*cos  (x)*sin (x) + 119759850*cos  (x)*sin  (x) + 119759850*cos  (x)*sin  (x)/*\cos  (x) - sin  (x) - 145422675*cos  (x)*sin  (x) - 86493225*cos  (x)*sin  (x) - 30045015*cos  (x)*sin  (x) - 5852925*cos (x)*sin  (x) - 593775*cos  (x)*sin (x) - 27405*cos (x)*sin  (x) - 435*cos  (x)*sin (x) + 435*cos (x)*sin  (x) + 27405*cos  (x)*sin (x) + 593775*cos (x)*sin  (x) + 5852925*cos  (x)*sin (x) + 30045015*cos  (x)*sin  (x) + 86493225*cos  (x)*sin  (x) + 145422675*cos  (x)*sin  (x)/

$$\left(30 \sin^{29}{\left (x \right )} \cos{\left (x \right )} - 4060 \sin^{27}{\left (x \right )} \cos^{3}{\left (x \right )} + 142506 \sin^{25}{\left (x \right )} \cos^{5}{\left (x \right )} - 2035800 \sin^{23}{\left (x \right )} \cos^{7}{\left (x \right )} + 14307150 \sin^{21}{\left (x \right )} \cos^{9}{\left (x \right )} - 54627300 \sin^{19}{\left (x \right )} \cos^{11}{\left (x \right )} + 119759850 \sin^{17}{\left (x \right )} \cos^{13}{\left (x \right )} - 155117520 \sin^{15}{\left (x \right )} \cos^{15}{\left (x \right )} + 119759850 \sin^{13}{\left (x \right )} \cos^{17}{\left (x \right )} - 54627300 \sin^{11}{\left (x \right )} \cos^{19}{\left (x \right )} + 14307150 \sin^{9}{\left (x \right )} \cos^{21}{\left (x \right )} - 2035800 \sin^{7}{\left (x \right )} \cos^{23}{\left (x \right )} + 142506 \sin^{5}{\left (x \right )} \cos^{25}{\left (x \right )} - 4060 \sin^{3}{\left (x \right )} \cos^{27}{\left (x \right )} + 30 \sin{\left (x \right )} \cos^{29}{\left (x \right )}\right) \left(- \sin^{30}{\left (x \right )} + 435 \sin^{28}{\left (x \right )} \cos^{2}{\left (x \right )} - 27405 \sin^{26}{\left (x \right )} \cos^{4}{\left (x \right )} + 593775 \sin^{24}{\left (x \right )} \cos^{6}{\left (x \right )} - 5852925 \sin^{22}{\left (x \right )} \cos^{8}{\left (x \right )} + 30045015 \sin^{20}{\left (x \right )} \cos^{10}{\left (x \right )} - 86493225 \sin^{18}{\left (x \right )} \cos^{12}{\left (x \right )} + 145422675 \sin^{16}{\left (x \right )} \cos^{14}{\left (x \right )} - 145422675 \sin^{14}{\left (x \right )} \cos^{16}{\left (x \right )} + 86493225 \sin^{12}{\left (x \right )} \cos^{18}{\left (x \right )} - 30045015 \sin^{10}{\left (x \right )} \cos^{20}{\left (x \right )} + 5852925 \sin^{8}{\left (x \right )} \cos^{22}{\left (x \right )} - 593775 \sin^{6}{\left (x \right )} \cos^{24}{\left (x \right )} + 27405 \sin^{4}{\left (x \right )} \cos^{26}{\left (x \right )} - 435 \sin^{2}{\left (x \right )} \cos^{28}{\left (x \right )} + \cos^{30}{\left (x \right )}\right)$$