Which expression corresponds to the cosine of the difference formula?

Which expression corresponds to the cosine of the difference formula?

• A. cosA + cosB
• B. cosAcosB - sinAsinB
• C. sinAcosB - cosAsinB
• D. cosAcosB + sinA + sinB

Answer: (B)

The cosine of the difference formula is given by the equation \( \cos(A - B) = \cos A \cos B + \sin A \sin B \). In the context of the options provided, the correct expression that corresponds to this formula is found in the choice which states \( \cos A \cos B - \sin A \sin B \). This formula states that to find the cosine of the difference between two angles \( A \) and \( B \), you should multiply the cosines of the angles together and then subtract the product of the sines of the angles. This reflects the relationship between cosine and the angles in a unit circle, where the cosine function captures the horizontal coordinates based on the angle measure. In summary, the selection that states \( \cos A \cos B - \sin A \sin B \) accurately represents the structure of the cosine difference formula, confirming that it is representative of the relation when subtracting one angle from another in trigonometric contexts.

The cosine of the difference formula is given by the equation ( \cos(A - B) = \cos A \cos B + \sin A \sin B ). In the context of the options provided, the correct expression that corresponds to this formula is found in the choice which states ( \cos A \cos B - \sin A \sin B ).

This formula states that to find the cosine of the difference between two angles ( A ) and ( B ), you should multiply the cosines of the angles together and then subtract the product of the sines of the angles. This reflects the relationship between cosine and the angles in a unit circle, where the cosine function captures the horizontal coordinates based on the angle measure.

In summary, the selection that states ( \cos A \cos B - \sin A \sin B ) accurately represents the structure of the cosine difference formula, confirming that it is representative of the relation when subtracting one angle from another in trigonometric contexts.