Question

Cos5a-cos3a=? cosa=0.6​

Answer 1

Ответ:

Применяем формулу разности косинусов .

$\bf cos5a-cos3a=-2\cdot sin\dfrac{5a-3a}{2}\cdot sin\dfrac{5a+3a}{2}=-2\cdot sina\cdot sin4a=\\\\\\=-2\cdot sina\cdot (2\, sin2a\cdot cos2a)=-2\cdot sina\cdot 2\cdot (\underbrace{\bf 2\, sina\cdot cosa}_{sin2a})\cdot (\underbrace{\bf 2cos^2a-1}_{cos2a})=\\\\\\=-8\cdot sin^2a\cdot cosa\cdot (2cos^2a-1)\ ;$  

Значение  sin²a  можно найти из формулы тригонометрической единицы :  

$\bf sin^2a+cos^2a=1\ \ \Rightarrow \ \ \ sin^2a=1-cos^2a$    

$\bf -8\cdot sin^2a\cdot cosa\cdot (2cos^2a-1)=-8\cdot (1-cos^2a)\cdot cosa\cdot (2cos^2a-1)=\\\\=-8\cdot (1-0,36)\cdot 0,6\cdot (2\cdot 0,36-1)=-8\cdot 0,64\cdot 0,6\cdot (-0,28)=0,86016$  

Answer 2

To find the value of cos(5a) - cos(3a), we can use the trigonometric identity:

cos(A) - cos(B) = -2 * sin((A + B)/2) * sin((A - B)/2)

Let's substitute A = 5a and B = 3a into the identity:

cos(5a) - cos(3a) = -2 * sin((5a + 3a)/2) * sin((5a - 3a)/2) = -2 * sin(4a) * sin(a)

Now, you mentioned that cos(a) = 0.6. We can use the Pythagorean identity sin^2(a) + cos^2(a) = 1 to find sin(a):

sin^2(a) + cos^2(a) = 1 sin^2(a) = 1 - cos^2(a) sin(a) = sqrt(1 - cos^2(a))

Plugging in cos(a) = 0.6:

sin(a) = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8

Now, we can substitute sin(a) = 0.8 back into the expression:

cos(5a) - cos(3a) = -2 * sin(4a) * sin(a) = -2 * sin(4a) * 0.8

Please note that the value of cos(5a) - cos(3a) depends on the value of sin(4a), which is not given in your question. If you provide the value of sin(4a), I can help you calculate the final result.