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If \( f(\alpha, \beta)=\cos ^{2} \alpha+\sin ^{2} \alpha \cdot \cos 2 \beta \), then which of the following is incorrect?
\( \mathrm{P} \)
(a) \( f\left(\frac{\pi}{5}, \frac{2 \pi}{5}\right) \neq f\left(\frac{2 \pi}{5}, \frac{\pi}{5}\right) \)
(b) \( f\left(\frac{\pi}{12}, \frac{\pi}{3}\right)=f\left(\frac{\pi}{3}, \frac{\pi}{12}\right) \)
(c) \( 3 f\left(\frac{\pi}{5}, \frac{\pi}{3}\right) \neq f\left(\frac{\pi}{3}, \frac{\pi}{5}\right) \)
(d) \( f\left(\frac{\pi}{4}, \frac{\pi}{18}\right) \neq 3 f\left(\frac{\pi}{18}, \frac{\pi}{4}\right) \)
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