The expression frac{tan(x - frac{pi}{2}) cdot | vedclass

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(D) Using trigonometric identities:$	an(x - \frac{\pi}{2}) = -\cot x$$\cos(\frac{3\pi}{2} + x) = \sin x$$\sin(\frac{7\pi}{2} - x) = \sin(4\pi - \frac

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$\sin^2 x$

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(D) Using trigonometric identities:$	an(x - \frac{\pi}{2}) = -\cot x$$\cos(\frac{3\pi}{2} + x) = \sin x$$\sin(\frac{7\pi}{2} - x) = \sin(4\pi - \frac{\pi}{2} - x) = \sin(-\frac{\pi}{2} - x) = -\cos x$$\cos(x - \frac{\pi}{2}) = \sin x$$	an(\frac{3\pi}{2} + x) = -\cot x$Substituting these into the expression:$= \frac{(-\cot x)(\sin x) - (-\cos x)^3}{(\sin x)(-\cot x)}$$= \frac{-\cos x + \cos^3 x}{-\sin x \cdot \frac{\cos x}{\sin x}}$$= \frac{\cos x(\cos^2 x - 1)}{-\cos x}$$= -(\cos^2 x - 1) = 1 - \cos^2 x = \sin^2 x$

The expression $\frac{\tan(x - \frac{\pi}{2}) \cdot \cos(\frac{3\pi}{2} + x) - \sin^3(\frac{7\pi}{2} - x)}{\cos(x - \frac{\pi}{2}) \cdot \tan(\frac{3\pi}{2} + x)}$ simplifies to:

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