Find the value of \(2\cos^2 60° + 3\sin^2 45° - 3\sin^2 30° + 2\cos^2 90°\).
Answer: B
Substitute the standard values:
\(2(\frac{1}{2})^2 + 3(\frac{1}{\sqrt{2}})^2 - 3(\frac{1}{2})^2 + 2(0)^2\)
= \(2(\frac{1}{4}) + 3(\frac{1}{2}) - 3(\frac{1}{4}) + 0\)
= \(\frac{1}{2} + \frac{3}{2} - \frac{3}{4}\)
= \(\frac{4}{2} - \frac{3}{4} = 2 - \frac{3}{4} = \frac{8-3}{4} = \frac{5}{4}\).