Which of the following expressions has the same value as $\tan (-45°)$?

• A. $-\cos (180°)$
• B. $\tan (45°)$
• C. $\cot (135°)$
• D. $-\sin (270°)$

Answer: (C)

Verified step by step guidance

1. Recall the definition of the tangent function for negative angles: \(\tan(-\theta) = -\tan(\theta)\). So, \(\tan(-45^\circ) = -\tan(45^\circ)\).
2. Evaluate \(\tan(45^\circ)\) using the known value: \(\tan(45^\circ) = 1\). Therefore, \(\tan(-45^\circ) = -1\).
3. Check each given expression to see which one equals \(-1\) by using known trigonometric values and identities:
4. For example, \(-\cos(180^\circ)\): since \(\cos(180^\circ) = -1\), then \(-\cos(180^\circ) = -(-1) = 1\), which is not equal to \(-1\).
5. Similarly, analyze \(\tan(45^\circ)\), \(\cot(135^\circ)\), and \(-\sin(270^\circ)\) by recalling their values or using identities to find which matches \(-1\).