Question

Sin3a-2cos3a/2sin3a+cos3a​

Answer 1

Объяснение:

всё правильно наверно

Answer 2

To simplify the expression $\frac{{\sin(3a) - 2\cos(3a)}}{{2\sin(3a) + \cos(3a)}}$, we can use trigonometric identities.

1. We'll start by expressing $\sin(3a)$ and $\cos(3a)$ in terms of $\sin(a)$ and $\cos(a)$ using the triple angle formulas:

   $\sin(3a) = 3\sin(a) - 4\sin^3(a)$

   $\cos(3a) = 4\cos^3(a) - 3\cos(a)$

2. Now, substitute these into the original expression:

   $\frac{{3\sin(a) - 4\sin^3(a) - 2(4\cos^3(a) - 3\cos(a))}}{{2(3\sin(a) - 4\sin^3(a)) + 4\cos^3(a) - 3\cos(a)}}$

3. Simplify further:

   $\frac{{3\sin(a) - 4\sin^3(a) - 8\cos^3(a) + 6\cos(a)}}{{6\sin(a) - 8\sin^3(a) + 4\cos^3(a) - 3\cos(a)}}$

4. Rearrange terms:

   $\frac{{3\sin(a) + 6\cos(a) - 4\sin^3(a) - 8\cos^3(a)}}{{6\sin(a) - 8\sin^3(a) + 4\cos^3(a) - 3\cos(a)}}$

5. Factor out common terms:

   $\frac{{3(\sin(a) + 2\cos(a)) - 4\sin^3(a) + 8\cos^3(a)}}{{3(2\sin(a) - 2\sin^3(a) + \frac{4}{3}\cos^3(a) - \cos(a))}}$

   $\frac{{\sin(a) + 2\cos(a) - 4\sin^3(a) + 8\cos^3(a)}}{{2\sin(a) - 2\sin^3(a) + \frac{4}{3}\cos^3(a) - \cos(a)}}$

That's the simplified form of the expression.