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

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(D) Using trigonometric identities:$1$. $	an(x - \frac{\pi}{2}) = -\cot x$$2$. $\cos(\frac{3\pi}{2} + x) = \sin x$$3$. $\sin(\frac{7\pi}{2} - x) = \s

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$\sin^2 x$

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(D) Using trigonometric identities:$1$. $	an(x - \frac{\pi}{2}) = -\cot x$$2$. $\cos(\frac{3\pi}{2} + x) = \sin x$$3$. $\sin(\frac{7\pi}{2} - x) = \sin(4\pi - \frac{\pi}{2} - x) = \sin(-\frac{\pi}{2} - x) = -\cos x$$4$. $\cos(x - \frac{\pi}{2}) = \sin x$$5$. $	an(\frac{3\pi}{2} + x) = -\cot x$Substituting these into the expression:Numerator: $(-\cot x)(\sin x) - (-\cos x)^3 = -\cos x + \cos^3 x = \cos x(\cos^2 x - 1) = -\cos x \sin^2 x$Denominator: $(\sin x)(-\cot x) = -\cos x$Expression: $\frac{-\cos x \sin^2 x}{-\cos x} = \sin^2 x$.

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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