Question

Cos7a-cos3a/sin5a=?

Answer 1

Ответ:

−  145259571246097 /10138971855420   ≈ −0.07

Answer 2

To simplify the expression (cos^7(a) - cos^3(a)) / sin^5(a), we'll use trigonometric identities. Specifically, we can apply the following trigonometric identities:

1. cos^2(a) = 1 - sin^2(a)
2. cos^3(a) = cos(a) * cos^2(a)
3. cos^4(a) = (cos^2(a))^2
4. cos^5(a) = cos(a) * (cos^4(a))
5. cos^6(a) = (cos^2(a)) * (cos^4(a))
6. cos^7(a) = cos(a) * (cos^6(a))

Let's proceed with the simplification step by step:

Expression: (cos^7(a) - cos^3(a)) / sin^5(a)

Step 1: Rewrite cos^3(a) using the identity cos^3(a) = cos(a) * cos^2(a) (cos^7(a) - cos(a) * cos^2(a)) / sin^5(a)

Step 2: Rewrite cos^2(a) using the identity cos^2(a) = 1 - sin^2(a) (cos^7(a) - cos(a) * (1 - sin^2(a))) / sin^5(a)

Step 3: Distribute the cos(a) term inside the brackets (cos^7(a) - cos(a) + cos(a) * sin^2(a)) / sin^5(a)

Step 4: Factor out cos(a) from the first two terms in the numerator cos(a) * (cos^6(a) - 1 + sin^2(a)) / sin^5(a)

Step 5: Use the identity cos^2(a) + sin^2(a) = 1 cos(a) * (cos^6(a) + sin^2(a)) / sin^5(a)

The expression is now simplified as cos(a) * (cos^6(a) + sin^2(a)) / sin^5(a).