Which expression has the same value as $\tan (-45°)$?

• A. $-\tan (45°)$
• B. $\tan (45°)$
• C. $\sin (45°)$
• D. $\cos (45°)$

Answer: (A)

Verified step by step guidance

1. Recall the definition of the tangent function and its behavior with negative angles. The tangent function is an odd function, which means that \(\tan(-\theta) = -\tan(\theta)\).
2. Apply this property to the given expression \(\tan(-45^\circ)\). Using the odd function property, rewrite it as \(-\tan(45^\circ)\).
3. Recognize that \(\tan(45^\circ)\) is a well-known value, but since the problem asks for an equivalent expression rather than a numeric value, keep it in symbolic form.
4. Compare the given options to the expression \(-\tan(45^\circ)\). The expression that matches this form is the one that has the same value as \(\tan(-45^\circ)\).
5. Understand why the other options (\(\tan(45^\circ)\), \(\sin(45^\circ)\), and \(\cos(45^\circ)\)) do not match the value of \(\tan(-45^\circ)\) based on the properties of tangent and the values of sine and cosine at \(45^\circ\).