Question

B) cos 3a + cos a;г) cos a - cos 7а;​

Answer 1

Ответ:

В) cos 4a

г) -cos 6a

Пошаговое объяснение:

Answer 2

It seems like you're asking about trigonometric expressions involving cosine functions. I'll be happy to help you with those expressions:

B) cos(3a) + cos(a): To simplify this expression, you can use trigonometric identities. One such identity is the sum-to-product identity, which states that: $\cos(x) + \cos(y) = 2 \cos\left(\frac{x + y}{2}\right) \cos\left(\frac{x - y}{2}\right)$

Applying this identity to the expression cos(3a) + cos(a), we have: $\cos(3a) + \cos(a) = 2 \cos\left(\frac{3a + a}{2}\right) \cos\left(\frac{3a - a}{2}\right)$

Simplifying: $\cos(3a) + \cos(a) = 2 \cos(2a) \cos(a)$

So, the simplified expression is $2 \cos(2a) \cos(a)$.

г) cos(a) - cos(7a): Similarly, we can use the difference-to-product identity, which states that: $\cos(x) - \cos(y) = -2 \sin\left(\frac{x + y}{2}\right) \sin\left(\frac{x - y}{2}\right)$

Applying this identity to the expression cos(a) - cos(7a), we have: $\cos(a) - \cos(7a) = -2 \sin\left(\frac{a + 7a}{2}\right) \sin\left(\frac{a - 7a}{2}\right)$

Simplifying: $\cos(a) - \cos(7a) = -2 \sin\left(\frac{8a}{2}\right) \sin\left(\frac{-6a}{2}\right)$ $\cos(a) - \cos(7a) = -2 \sin(4a) \sin(-3a)$ $\cos(a) - \cos(7a) = 2 \sin(4a) \sin(3a)$

So, the simplified expression is $2 \sin(4a) \sin(3a)$.

Please note that these are the simplified forms of the given expressions using trigonometric identities. If you have specific values for 'a' or if you need further assistance, please provide more information.