tan 45° = 1, cos 60° = 1/2
$\frac{1}{2}\tan^2 45° - \cos^2 60° = \frac{1}{2}(1)^2 - \left(\frac{1}{2}\right)^2 = \frac{1}{2} - \frac{1}{4} = \frac{1}{4}$
Answer: (C) $\dfrac{1}{4}$
Substitute standard values from Table 8.1 (Chapter 8, Section 8.3): tan 45° = 1 and cos 60° = ½. Apply the formula directly — the key step students miss is the ½ coefficient before tan²45°, which gives ½ × 1 = ½, not 1.