What does the cosine of the difference of two angles represent?

What does the cosine of the difference of two angles represent?

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

Answer: (C)

The cosine of the difference of two angles, specifically represented as cos(A - B), is defined by the formula cos(A - B) = cosAcosB + sinAsinB. This relationship is derived from trigonometric identities and reflects how the cosine function behaves when working with the difference of two angles. When breaking down this formula, it illustrates that the cosine of the angle difference is made up of two components: the product of the cosines of the angles and the product of the sines of the angles. This identity is particularly useful in various applications, including simplifying trigonometric expressions and solving equations involving angles. Understanding this identity is crucial when you encounter problems involving angle differences in trigonometry, as it allows for transformations and evaluations of angles that might not be easily calculable otherwise.

The cosine of the difference of two angles, specifically represented as cos(A - B), is defined by the formula cos(A - B) = cosAcosB + sinAsinB. This relationship is derived from trigonometric identities and reflects how the cosine function behaves when working with the difference of two angles.

When breaking down this formula, it illustrates that the cosine of the angle difference is made up of two components: the product of the cosines of the angles and the product of the sines of the angles. This identity is particularly useful in various applications, including simplifying trigonometric expressions and solving equations involving angles.

Understanding this identity is crucial when you encounter problems involving angle differences in trigonometry, as it allows for transformations and evaluations of angles that might not be easily calculable otherwise.