Chapter 4 - Section 4.3 - Right Triangle Trigonometry - Exercise Set - Page 563: 77

False.

Please note that $\tan^2 x$ does not equal $\tan x^2$. We have$$\tan 5^{\circ } \approx 0.087 \quad \Rightarrow \quad \tan^2 5^{ \circ } \approx 0.008 \\ \tan 25^{\circ } \approx 0.466 \\ \Rightarrow \quad \tan^2 5^{\circ } \neq \tan 25^{\circ}.$$