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cos((3pi)/(2) +x) cos(2pi+x)[cot(3pi)/(2...

`cos((3pi)/(2) +x) cos(2pi+x)[cot(3pi)/(2)-x+cot(2pi+x)]=1`

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To solve the equation \( \cos\left(\frac{3\pi}{2} + x\right) \cos(2\pi + x) \left[\cot\left(\frac{3\pi}{2} - x\right) + \cot(2\pi + x)\right] = 1 \), we will simplify the left-hand side step by step. ### Step 1: Simplifying \( \cos\left(\frac{3\pi}{2} + x\right) \) Using the cosine addition formula, we have: \[ \cos\left(\frac{3\pi}{2} + x\right) = \cos\left(\frac{3\pi}{2}\right)\cos(x) - \sin\left(\frac{3\pi}{2}\right)\sin(x) \] Since \( \cos\left(\frac{3\pi}{2}\right) = 0 \) and \( \sin\left(\frac{3\pi}{2}\right) = -1 \): ...
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