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

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If \( \cot \alpha=1 \) and \( \sec \beta=-\frac{5}{3} \), where \( \pi\alpha\frac{3 \pi}{2} \) and, \( \frac{\pi}{2} \) \( \beta\pi \) then the value of \( \tan (\alpha+\beta) \) and the quadrant in which \( \alpha+\beta \) lies, respectively are
(a) \( -\frac{1}{7} \) and IV \( { }^{\text {th }} \) quadrant
(b) 7 and I It \( ^{\text {st }} \) quadrant
(c) -7 and IV \( ^{\text {th }} \) quadrant
(d) \( \frac{1}{7} \) and It \( ^{\mathrm{st}} \) quadrant
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