The value of (sin² 45° . cos² 45°) + (5tan² 30°) + \(\frac{3}{2}\)sin² 90° - 3cos² 30°

1

(sin² 45° . cos² 45°) + (5tan² 30°) + \(\frac{3}{2}\)sin² 90° - 3cos² 30°

= (\(\frac{1}{2}\) . \(\frac{1}{2}\)) + 5(\(\frac{1}{\sqrt {3 }}\))² + \(\frac{3}{2}\)(1)² - 3( \(\frac{3}{4}\))

= \(\frac{1}{4}\) + \(\frac{5}{3}\) + \(\frac{3}{2}\) - \(\frac{9}{4}\)

= \(\frac{3 + 30 + 18 - 27}{24}\)

= \(\frac{24}{24}\)

= 1