Question

1) 4cos 5a sin 5a cos10a​

Answer 1

Ответ:в прикреплённом файле

Пошаговое объяснение:

Answer 2

To simplify the expression $4\cos(5a) \sin(5a) \cos(10a)$, you can use trigonometric identities.

Recall the double-angle trigonometric identity:

$\cos(2x) = 2\cos^2(x) - 1$

Now, let's use this identity to simplify the expression step by step:

1. Start with the original expression:

   $4\cos(5a) \sin(5a) \cos(10a)$

2. Notice that $\cos(10a)$ can be rewritten as $\cos(2 \cdot 5a)$, so we can use the double-angle identity:

   $\cos(10a) = 2\cos^2(5a) - 1$

3. Substitute this back into the expression:

   $4\cos(5a) \sin(5a) (2\cos^2(5a) - 1)$

4. Now, simplify further:

   $8\cos^2(5a) \sin(5a) - 4\cos(5a) \sin(5a)$

5. Factor out a common term of $\sin(5a)$:

   $4\sin(5a)(2\cos^2(5a) - 1)$

So, the simplified expression is $4\sin(5a)(2\cos^2(5a) - 1)$.