If $\cot \alpha=1$ and $\sec \beta=-\frac{5}{3}$, where $\pi

Question

If $\cot \alpha=1$ and $\sec \beta=-\frac{5}{3}$, where $\pi<\alpha<\frac{3 \pi}{2}$ and, $\frac{\pi}{2}$ $<\beta<\pi$, then the value of $\tan (\alpha+\beta)$ and the quadrant in which $\alpha+\beta$ lies, respectively are [JEE Main 2022, 28 June (Shift 2)]

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If \(\cot \alpha=1\) and \(\sec \beta=-\frac{5}{3}\), where \(\pi<\alpha<\frac{3 \pi}{2}\) and, \(\frac{\pi}{2}\) …

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If \(\cot \alpha=1\) and \(\sec \beta=-\frac{5}{3}\), where \(\pi&lt;\alpha&lt;\frac{3 \pi}{2}\) and, \(\frac{\pi}{2}\) …

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If \(\cot \alpha=1\) and \(\sec \beta=-\frac{5}{3}\), where \(\pi<\alpha<\frac{3 \pi}{2}\) and, \(\frac{\pi}{2}\) …