<s>[INST] Is equality $\sin(\frac{3\pi}{2}-x) = -\cos(x)$ always true? $\sin(\frac{3\pi}{2}-x) = -\cos(x)$
Is above equality always true even if $x \gt \frac{\pi}{2}$?
 [/INST] why not $$\sin\left(\frac{3\pi} 2 - x\right) = \sin \left(\frac{3\pi} 2\right)\cos x -\cos\left(\frac{3\pi} 2\right) \sin x = -\cos x?$$
</s>