Find the value of $$\sin^230 \cos^245 + 4 \tan^230 + (1/2) \sin^290 - \cos^290 + 1/24$$

$$\sin^230 \cos^245 + 4 \tan^230 + (1/2) \sin^290 - \cos^290 + 1/24$$

By trigonometric ratio,

$$\left(\frac{1}{2}\right)^2\times\ \left(\frac{1}{\sqrt{\ 2}}\right)^2+4\left(\frac{1}{\sqrt{\ 3}}\right)^2+\frac{1}{2}\left(1\right)^2-\left(0\right)^2+\frac{1}{24}$$

$$\frac{1}{4}\times\ \frac{1}{2}+4\times\ \frac{1}{3}+\frac{1}{2}-0+\frac{1}{24}$$

$$\frac{1}{8}+\frac{4}{3}+\frac{1}{2}+\frac{1}{24}=\frac{48}{24}=2$$.