Question

Sin2a*cosa-cos2a*sina​

Answer 1

Ответ:

Пошаговое объяснение:

sin2a*cosa-cos2a*sina​=sin(2a-a)=sina

Answer 2

To simplify the expression sin(2a) * cos(a) - cos(2a) * sin(a), we can apply trigonometric identities.

First, let's expand the expression using the double-angle identities:

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

Substituting these values back into the expression:

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

Expanding further:

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

Now, we can simplify it by factoring out sin(a):

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

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

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

Simplifying further:

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

Combining like terms:

sin(a) * (1)

Finally, the simplified expression is:

sin(a)