Find the value of (8sin45° + 5cos60°)/(sin^230° - 2cos^245° + 7tan45°)

\(\frac{8sin45° + 5 cos60°}{sin^230° - 2cos^245° + 7tan45°}\)

= \(\frac{\frac{8}{\sqrt{2}} + \frac{5}{2}}{\frac{1}{4} - 2 × \frac{1}{2} + 7}\)

= \(\frac{4\sqrt {2} + \frac{5}{2}}{\frac{1}{4} + 6}\)

= \(\frac{2(8\sqrt {2} + 5)}{25}\)

= \(\frac{2(5 + 8\sqrt {2})}{25}\)