The value of \((\cos^2 67° - \sin^2 23°) + 4\cos 30°\) is:
\(2\sqrt{3}\)
Use the complementary-angle identity \(\sin\theta = \cos(90° - \theta)\).
Since \(\sin 23° = \cos(90° - 23°) = \cos 67°\), we get \(\sin^2 23° = \cos^2 67°\).
Therefore \(\cos^2 67° - \sin^2 23° = 0\).
The expression becomes \(0 + 4\cos 30° = 4 \times \frac{\sqrt{3}}{2} = 2\sqrt{3}\).
Hence, the value of the expression is \(2\sqrt{3}\).
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