3 cos a если sin a – Найдите 3cos a, если sin a = -2корня из двух/3 и a…

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

Решение

   3                3          
cos (a)*sin(a) - sin (a)*cos(a)

$$- \sin^{3}{\left (a \right )} \cos{\left (a \right )} + \sin{\left (a \right )} \cos^{3}{\left (a \right )}$$

Подстановка условия

[LaTeX]

cos(a)^3*sin(a) - sin(a)^3*cos(a) при a = -3/2
cos(a)^3*sin(a) - sin(a)^3*cos(a)

$$- \sin^{3}{\left (a \right )} \cos{\left (a \right )} + \sin{\left (a \right )} \cos^{3}{\left (a \right )}$$

cos((-3/2))^3*sin((-3/2)) - sin((-3/2))^3*cos((-3/2))

$$- \sin^{3}{\left ((-3/2) \right )} \cos{\left ((-3/2) \right )} + \sin{\left ((-3/2) \right )} \cos^{3}{\left ((-3/2) \right )}$$

cos(-3/2)^3*sin(-3/2) - sin(-3/2)^3*cos(-3/2)

$$\sin{\left (- \frac{3}{2} \right )} \cos^{3}{\left (- \frac{3}{2} \right )} — \sin^{3}{\left (- \frac{3}{2} \right )} \cos{\left (- \frac{3}{2} \right )}$$

sin(3/2)^3*cos(3/2) - cos(3/2)^3*sin(3/2)

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

Численный ответ

[LaTeX]

cos(a)^3*sin(a) - sin(a)^3*cos(a)
Объединение рациональных выражений

[LaTeX]

/   2         2   \              
\cos (a) - sin (a)/*cos(a)*sin(a)

$$\left(- \sin^{2}{\left (a \right )} + \cos^{2}{\left (a \right )}\right) \sin{\left (a \right )} \cos{\left (a \right )}$$

Общее упрощение

[LaTeX]

$$\frac{1}{4} \sin{\left (4 a \right )}$$

Собрать выражение

[LaTeX]

$$\frac{1}{4} \sin{\left (4 a \right )}$$

Тригонометрическая часть

[LaTeX]

$$\frac{1}{4} \sin{\left (4 a \right )}$$

Комбинаторика

[LaTeX]

(-sin(a) + cos(a))*(cos(a) + sin(a))*cos(a)*sin(a)

$$\left(- \sin{\left (a \right )} + \cos{\left (a \right )}\right) \left(\sin{\left (a \right )} + \cos{\left (a \right )}\right) \sin{\left (a \right )} \cos{\left (a \right )}$$

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

Решение

   3                3          
sin (a)*cos(a) + cos (a)*sin(a)

$$\sin^{3}{\left (a \right )} \cos{\left (a \right )} + \sin{\left (a \right )} \cos^{3}{\left (a \right )}$$

Подстановка условия

[LaTeX]

sin(a)^3*cos(a) + cos(a)^3*sin(a) при a = -3/2
sin(a)^3*cos(a) + cos(a)^3*sin(a)

$$\sin^{3}{\left (a \right )} \cos{\left (a \right )} + \sin{\left (a \right )} \cos^{3}{\left (a \right )}$$

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

$$\sin^{3}{\left ((-3/2) \right )} \cos{\left ((-3/2) \right )} + \sin{\left ((-3/2) \right )} \cos^{3}{\left ((-3/2) \right )}$$

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

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

-cos(3/2)^3*sin(3/2) - sin(3/2)^3*cos(3/2)

$$- \sin^{3}{\left (\frac{3}{2} \right )} \cos{\left (\frac{3}{2} \right )} — \sin{\left (\frac{3}{2} \right )} \cos^{3}{\left (\frac{3}{2} \right )}$$

Численный ответ

[LaTeX]

cos(a)^3*sin(a) + sin(a)^3*cos(a)
Объединение рациональных выражений

[LaTeX]

/   2         2   \              
\cos (a) + sin (a)/*cos(a)*sin(a)

$$\left(\sin^{2}{\left (a \right )} + \cos^{2}{\left (a \right )}\right) \sin{\left (a \right )} \cos{\left (a \right )}$$

Общее упрощение

[LaTeX]

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

Собрать выражение

[LaTeX]

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

Тригонометрическая часть

[LaTeX]

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

Комбинаторика

[LaTeX]

/   2         2   \              
\cos (a) + sin (a)/*cos(a)*sin(a)

$$\left(\sin^{2}{\left (a \right )} + \cos^{2}{\left (a \right )}\right) \sin{\left (a \right )} \cos{\left (a \right )}$$

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

Решение

cos(a) + sin(a)
---------------
cos(a) - sin(a)

$$\frac{\sin{\left (a \right )} + \cos{\left (a \right )}}{- \sin{\left (a \right )} + \cos{\left (a \right )}}$$

Подстановка условия

[LaTeX]

(cos(a) + sin(a))/(cos(a) - sin(a)) при a = 3
(cos(a) + sin(a))/(cos(a) - sin(a))

$$\frac{\sin{\left (a \right )} + \cos{\left (a \right )}}{- \sin{\left (a \right )} + \cos{\left (a \right )}}$$

(cos((3)) + sin((3)))/(cos((3)) - sin((3)))

$$\frac{\sin{\left ((3) \right )} + \cos{\left ((3) \right )}}{- \sin{\left ((3) \right )} + \cos{\left ((3) \right )}}$$

(cos(3) + sin(3))/(cos(3) - sin(3))

$$\frac{\cos{\left (3 \right )} + \sin{\left (3 \right )}}{\cos{\left (3 \right )} — \sin{\left (3 \right )}}$$

(cos(3) + sin(3))/(-sin(3) + cos(3))

$$\frac{\cos{\left (3 \right )} + \sin{\left (3 \right )}}{\cos{\left (3 \right )} — \sin{\left (3 \right )}}$$

Численный ответ

[LaTeX]

(cos(a) + sin(a))/(-sin(a) + cos(a))
Общее упрощение

[LaTeX]

$$\tan{\left (a + \frac{\pi}{4} \right )}$$

Общий знаменатель

[LaTeX]

        2*sin(a)    
1 + ----------------
    -sin(a) + cos(a)

$$1 + \frac{2 \sin{\left (a \right )}}{- \sin{\left (a \right )} + \cos{\left (a \right )}}$$

Тригонометрическая часть

[LaTeX]

$$\tan{\left (a + \frac{\pi}{4} \right )}$$

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(3+cos(a))*(3-cos(a))+(3-sin(a))*(3+sin(a)) если a=2 (упростите выражение)

Решение

(3 + cos(a))*(3 - cos(a)) + (3 - sin(a))*(3 + sin(a))

$$\left(- \sin{\left (a \right )} + 3\right) \left(\sin{\left (a \right )} + 3\right) + \left(- \cos{\left (a \right )} + 3\right) \left(\cos{\left (a \right )} + 3\right)$$

Подстановка условия

[LaTeX]

(3 + cos(a))*(3 - cos(a)) + (3 - sin(a))*(3 + sin(a)) при a = 2
(3 + cos(a))*(3 - cos(a)) + (3 - sin(a))*(3 + sin(a))

$$\left(- \sin{\left (a \right )} + 3\right) \left(\sin{\left (a \right )} + 3\right) + \left(- \cos{\left (a \right )} + 3\right) \left(\cos{\left (a \right )} + 3\right)$$

(3 + cos((2)))*(3 - cos((2))) + (3 - sin((2)))*(3 + sin((2)))

$$\left(- \sin{\left ((2) \right )} + 3\right) \left(\sin{\left ((2) \right )} + 3\right) + \left(- \cos{\left ((2) \right )} + 3\right) \left(\cos{\left ((2) \right )} + 3\right)$$

(3 + cos(2))*(3 - cos(2)) + (3 - sin(2))*(3 + sin(2))

$$\left(- \sin{\left (2 \right )} + 3\right) \left(\sin{\left (2 \right )} + 3\right) + \left(- \cos{\left (2 \right )} + 3\right) \left(\cos{\left (2 \right )} + 3\right)$$

(3 - cos(2))*(3 + cos(2)) + (3 - sin(2))*(3 + sin(2))

$$\left(- \sin{\left (2 \right )} + 3\right) \left(\sin{\left (2 \right )} + 3\right) + \left(- \cos{\left (2 \right )} + 3\right) \left(\cos{\left (2 \right )} + 3\right)$$

Численный ответ

[LaTeX]

(3.0 - cos(a))*(3.0 + cos(a)) + (3.0 - sin(a))*(3.0 + sin(a))
Общее упрощение

[LaTeX]

$$17$$

Собрать выражение

[LaTeX]

$$17$$

Общий знаменатель

[LaTeX]

        2         2   
18 - cos (a) - sin (a)

$$- \sin^{2}{\left (a \right )} — \cos^{2}{\left (a \right )} + 18$$

Тригонометрическая часть

[LaTeX]

$$17$$

Комбинаторика

[LaTeX]

        2         2   
18 - cos (a) - sin (a)

$$- \sin^{2}{\left (a \right )} — \cos^{2}{\left (a \right )} + 18$$

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