Evaluate each of the following:sin2 30° cos2 45° + 4 tan2 30° +

1.	Evaluate each of the following:sin2 30° cos2 45° + 4 tan2 30° + \(\frac{1}2\) sin2 90° - 2 cos2 90° + \(\frac{1}{24}\) cos2 0°
Answer» sin² 30° cos² 45° + 4 tan² 30° + \(\frac{1}2\) sin² 90° - 2 cos² 90° + \(\frac{1}{24}\) cos² 0° = \((\frac{1}2)^2\) x \((\frac{1}{\sqrt2})^2\) + 4 x \((\frac{1}{\sqrt3})^2\) + \(\frac{1}2\) x (1)²- 2 x (0)² + \(\frac{1}{24}\) x (1)² = \(\frac{1}4\)x \(\frac{1}2\) + \(\frac{4}3\) + \(\frac{1}2\) - 0 = \(\frac{1}{24}\) = \(\frac{1}8\) + \(\frac{4}3\) + \(\frac{1}2\) + \(\frac{1}{24}\) = 2

Evaluate each of the following:sin2 30° cos2 45° + 4 tan2 30° + \(\frac{1}2\) sin2 90° - 2 cos2 90° + \(\frac{1}{24}\) cos2 0°

Answer»

sin² 30° cos² 45° + 4 tan² 30° + \(\frac{1}2\) sin² 90° - 2 cos² 90° + \(\frac{1}{24}\) cos² 0°

= \((\frac{1}2)^2\) x \((\frac{1}{\sqrt2})^2\) + 4 x \((\frac{1}{\sqrt3})^2\) + \(\frac{1}2\) x (1)²- 2 x (0)² + \(\frac{1}{24}\) x (1)²

= \(\frac{1}4\)x \(\frac{1}2\) + \(\frac{4}3\) + \(\frac{1}2\) - 0 = \(\frac{1}{24}\)

= \(\frac{1}8\) + \(\frac{4}3\) + \(\frac{1}2\) + \(\frac{1}{24}\) = 2