Question

A) sin 2a*cosa - cos 2a sina​

Answer 1

Ответ:

Sin (2a-a) = sina

Пошаговое объяснение:

Answer 2

To simplify the given expression, we can use trigonometric identities to rewrite the terms. The most useful identity for this expression is:

sin(2a) = 2 * sin(a) * cos(a) cos(2a) = cos^2(a) - sin^2(a) = 1 - 2 * sin^2(a) (using the Pythagorean identity: cos^2(a) + sin^2(a) = 1)

Let's substitute these identities into the original expression:

A) sin(2a) * cos(a) - cos(2a) * sin(a)

Using the trigonometric identities:

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

Now, we simplify further:

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

Next, we can factor out sin(a):

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

Using the Pythagorean identity: cos^2(a) + sin^2(a) = 1

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

sin(a) * 1

The final simplified expression is:

A) sin(a)