Match each expression in Column I with its equivalent expression in Column II.

sin 60° cos 45° - cos 60° sin 45°

Verified step by step guidance

1. Recognize that the expression given is of the form \(\sin A \cos B - \cos A \sin B\), which matches the sine difference identity.
2. Recall the sine difference identity: \(\sin A \cos B - \cos A \sin B = \sin (A - B)\).
3. Identify the angles: \(A = 60^\circ\) and \(B = 45^\circ\).
4. Apply the identity to rewrite the expression as \(\sin (60^\circ - 45^\circ)\).
5. Simplify the angle inside the sine function to get \(\sin 15^\circ\), which is the equivalent expression.

Key Concepts

Sine of a Difference Formula

The sine of a difference of two angles, sin(A - B), is given by sin A cos B minus cos A sin B. This identity allows the expression sin 60° cos 45° - cos 60° sin 45° to be recognized as sin(60° - 45°), simplifying the evaluation.

Basic Trigonometric Values

Knowing the exact values of sine and cosine for common angles like 45° and 60° is essential. For example, sin 45° = cos 45° = √2/2, sin 60° = √3/2, and cos 60° = 1/2. These values help in simplifying and verifying trigonometric expressions.

Trigonometric Expression Matching

Matching expressions involves recognizing equivalent forms using identities and simplifications. Understanding how to rewrite expressions using formulas like angle sum/difference helps in pairing expressions from different columns correctly.