Evaluate each of the following: sin^2 30° cos^2 45° + 4 tan^2 30° + 1/2 sin^2 90° - 2 cos^2 90°

Question

Evaluate each of the following: 

sin² 30° cos² 45° + 4 tan² 30° + \(\frac{1}{2}\)sin² 90° - 2cos² 90° + \(\frac{1}{24}\) cos²90°

Answer 1

sin² 30° cos² 45° + 4 tan² 30° + \(\frac{1}{2}\)sin² 90° - 2cos² 90° + \(\frac{1}{24}\) cos²90°

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

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