If \(\sin^4 x+\cos^4 x=1\), where \(0 \le x \le \dfrac{\pi}{2}\), then what is \(\sin x \cdot \cos x\) equal to?
0
\(\sin^4x+\cos^4x=(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x=1-2\sin^2x\cos^2x\). Setting this equal to 1 gives \(2\sin^2x\cos^2x=0\), so \(\sin x\cos x=0\). The correct option is (a).
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