1.3 Using your comparison in Question 1.2, what general conclusion can be made regarding $$ \cos (A-B), \cos A-\cos B $$ and $$ \cos A \cdot \cos B+\sin A \cdot \sin B $$ for any values of A and B ? QUESTION 2

Question

UpStudy AI · Accepted Answer

To analyze the expressions $$ \cos(A - B) $$, $$ \cos A - \cos B $$, and $$ \cos A \cdot \cos B + \sin A \cdot \sin B $$, we can start by recalling the cosine subtraction formula:

$$
\cos(A - B) = \cos A \cdot \cos B + \sin A \cdot \sin B
$$

This means that the expression $$ \cos(A - B) $$ is equal to $$ \cos A \cdot \cos B + \sin A \cdot \sin B $$.

Now, let's compare $$ \cos(A - B) $$ with $$ \cos A - \cos B $$:

1. **Equality of Expressions**:
   - From the cosine subtraction formula, we have:
     $$
     \cos(A - B) = \cos A \cdot \cos B + \sin A \cdot \sin B
     $$
   - Therefore, we can conclude that:
     $$
     \cos(A - B) \neq \cos A - \cos B
     $$
   - The expression $$ \cos A - \cos B $$ does not equal $$ \cos(A - B) $$ in general.

2. **General Conclusion**:
   - The expression $$ \cos(A - B) $$ is equal to $$ \cos A \cdot \cos B + \sin A \cdot \sin B $$.
   - The difference $$ \cos A - \cos B $$ does not have a direct relationship with $$ \cos(A - B) $$ and can vary depending on the values of $$ A $$ and $$ B $$.

In summary, the general conclusion is:
- $$ \cos(A - B) = \cos A \cdot \cos B + \sin A \cdot \sin B $$
- $$ \cos A - \cos B $$ is not equal to $$ \cos(A - B) $$ and does not represent the same relationship.

If you have any specific values for $$ A $$ and $$ B $$ or further questions, feel free to ask!
$$ \cos(A - B) = \cos A \cdot \cos B + \sin A \cdot \sin B $$, and $$ \cos A - \cos B $$ is not equal to $$ \cos(A - B) $$.

1.3 Using your comparison in Question 1.2, what general conclusion can be made regarding \( \cos (A-B), \cos A-\cos B \) and \( \cos A \cdot \cos B+\sin A \cdot \sin B \) for any values of A and B ? QUESTION 2

Solución de tutoría real

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Trigonometry Questions