Match each expression in Column I with the correct...

Match each expression in Column I with the correct expression in Column II to form an identity.
(II)
A. $\sin A \cos B-\cos A \sin B$
B. $\frac{\tan A+\tan B}{1-\tan A \tan B}$
C. $\frac{\tan A-\tan B}{1+\tan A \tan B}$
D. $\sin A \cos B+\cos A \sin B$
(I)
$$\tan (A+B)$$

Key Concepts

Tangent Subtraction Formula

The tangent subtraction formula, defined as tan(A-B) = (tanA - tanB) / (1 + tanA·tanB), expresses the tangent of the difference between two angles in terms of the tangents of the individual angles. It is an important tool for simplifying and working through trigonometric problems involving differences of angles.

Tangent Addition Formula

The tangent addition formula, which states that tan(A+B) = (tanA + tanB) / (1 - tanA·tanB), relates the tangent of the sum of two angles to the tangents of the individual angles. This identity is useful for simplifying expressions and solving equations involving tangent functions.

Sine Addition Formula

The sine addition formula, expressed as sin(A+B) = sinA·cosB + cosA·sinB, is used to expand the sine of a sum of two angles. It plays a central role in transforming and simplifying trigonometric expressions that involve angle sums.

Trigonometric Identities

Trigonometric identities are equations involving trigonometric functions that hold true for all values of the involved variables within their domains. They are essential for simplifying expressions, proving equations, and solving problems in trigonometry.

Sine Subtraction Formula

The sine subtraction formula, given by sin(A-B) = sinA·cosB - cosA·sinB, is applied to express the sine of the difference of two angles. This formula is key in both solving trigonometric equations and verifying other trigonometric identities.

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