Evaluate without using trigonometric tables,

sin² 28° + sin² 62° + tan² 38° - cot² 52° + $\dfrac{1}{4} \text{sec}^2 \space 30°$

Solving,

⇒ sin² 28° + sin² 62° + tan² 38° - cot² 52° + $\dfrac{1}{4} \text{sec}^2 \space 30°$

⇒ sin² 28° + sin² (90° - 28°) + tan² (90° - 52°) - cot² 52° + $\dfrac{1}{4} \times \Big(\dfrac{2}{\sqrt{3}}\Big)^2$

By formula,

sin(90° - θ) = cos θ and tan(90° - θ) = cot θ

⇒ sin² 28° + cos² 28° + cot² 52° - cot² 52° + $\dfrac{1}{4} \times \dfrac{4}{3}$

By formula,

sin² θ + cos² θ = 1

⇒ 1 + $\dfrac{1}{3}$

⇒ $1\dfrac{1}{3}$.

Hence, sin² 28° + sin² 62° + tan² 38° - cot² 52° + $\dfrac{1}{4} \text{sec}^2 30° = 1\dfrac{1}{3}$.