1) Simplify: $$ \cos 2 u \cos 7 u-\sin 2 u \sin 7 u $$ a) $$ \cos 9 u $$ b) $$ \cos 5 u $$ c) $$ \sin 9 u $$ d) $$ \sin 5 u $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$ \cos 2u \cos 7u - \sin 2u \sin 7u $$, we can use the cosine addition formula:

$$
\cos(a + b) = \cos a \cos b - \sin a \sin b
$$

In our case, we can identify $$ a = 2u $$ and $$ b = 7u $$. Therefore, we can rewrite the expression as:

$$
\cos(2u + 7u) = \cos(9u)
$$

Thus, the simplified form of the expression $$ \cos 2u \cos 7u - \sin 2u \sin 7u $$ is:

$$
\cos 9u
$$

The correct answer is:

$$
\boxed{\cos 9u}
$$
$$\cos 9u$$

1) Simplify: \( \cos 2 u \cos 7 u-\sin 2 u \sin 7 u \) a) \( \cos 9 u \) b) \( \cos 5 u \) c) \( \sin 9 u \) d) \( \sin 5 u \)