The numerical value of $$\frac{cos^2 45\circ}{sin^2 60\circ}+\frac{cos^2 60\circ}{sin^2 45\circ}-\frac{tan^230\circ}{cot^245\circ}-\frac{sin^230\circ}{cot^230\circ}$$ is

Expression : $$\frac{cos^2 45}{sin^2 60}+\frac{cos^2 60}{sin^2 45}-\frac{tan^230}{cot^245}-\frac{sin^230}{cot^230}$$

= $$\frac{(\frac{1}{\sqrt{2}})^2}{(\frac{\sqrt{3}}{2})^2} + \frac{(\frac{1}{2})^2}{(\frac{1}{\sqrt{2}})^2} - \frac{(\frac{1}{\sqrt{3}})^2}{(1)^2} - \frac{(\frac{1}{2})^2}{(\sqrt{3})^2}$$

= $$(\frac{1}{2} \times \frac{4}{3}) + (\frac{1}{4} \times 2) - (\frac{1}{3} \times 1) - (\frac{1}{4 \times 3})$$

= $$\frac{2}{3} + \frac{1}{2} - \frac{1}{3} - \frac{1}{12}$$

= $$\frac{9}{12} = \frac{3}{4}$$