Find the values of :

sin² 60° - cos² 45° + 3 tan² 30°

Solving,

$\Rightarrow \Big(\dfrac{\sqrt{3}}{2}\Big)^2 - \Big(\dfrac{1}{\sqrt{2}}\Big)^2 + 3 \Big(\dfrac{1}{\sqrt{3}}\Big)^2 \\[1em] \Rightarrow \dfrac{3}{4} - \dfrac{1}{2} + 3 \times \dfrac{1}{3} \\[1em] \Rightarrow \dfrac{3 - 2}{4} + 1 \\[1em] \Rightarrow \dfrac{1}{4} + 1 \\[1em] \Rightarrow \dfrac{1 + 4}{4} \\[1em] \Rightarrow \dfrac{5}{4} \\[1em] \Rightarrow 1\dfrac{1}{4}.$

Hence, sin² 60° - cos² 45° + 3 tan² 30° = $1\dfrac{1}{4}$.