Question

(1-cos8x)/sin 8x упростить

Answer 1

Решение задания приложено

Answer 2

Решение во вложении.

Answer 3

To simplify the expression (1 - cos(8x)) / sin(8x), we can use trigonometric identities. One of the most relevant identities for this simplification is:

sin^2(x) + cos^2(x) = 1

Now, we can manipulate the expression as follows:

(1 - cos(8x)) / sin(8x) = (1 - cos^2(8x)) / sin(8x)

Using the identity sin^2(x) + cos^2(x) = 1, we can replace cos^2(8x) with (1 - sin^2(8x)):

(1 - cos^2(8x)) / sin(8x) = (1 - (1 - sin^2(8x))) / sin(8x)

Simplifying the numerator:

(1 - (1 - sin^2(8x))) / sin(8x) = (1 - 1 + sin^2(8x)) / sin(8x) = sin^2(8x) / sin(8x)

Finally, we can cancel out sin(8x) from the numerator and denominator:

sin^2(8x) / sin(8x) = sin(8x)

Therefore, the simplified expression is sin(8x).