1. The problem is to simplify $\sin\left(\frac{3\pi}{2} - x\right)$.\n\n2. We use the sine difference identity: $\sin(a - b) = \sin a \cos b - \cos a \sin b$.\n\n3. Applying this identity, we get:\n$$\sin\left(\frac{3\pi}{2} - x\right) = \sin\frac{3\pi}{2} \cos x - \cos\frac{3\pi}{2} \sin x.$$\n\n4. Evaluate $\sin\frac{3\pi}{2}$ and $\cos\frac{3\pi}{2}$:\n- $\sin\frac{3\pi}{2} = -1$\n- $\cos\frac{3\pi}{2} = 0$\n\n5. Substitute these values back:\n$$\sin\left(\frac{3\pi}{2} - x\right) = (-1) \cdot \cos x - 0 \cdot \sin x = -\cos x.$$\n\n6. Therefore, the simplified form is $-\cos x$.\n\nAnswer: d. $-\cos x$