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

• A. $-\frac{1}{7}$ and $IV ^{\text{ th }}$ quadrant
• B. 7 and $I ^{\text {st }}$ quadrant
• C. $-7$ and $IV ^{\text {th }}$ quadrant
• D. $\frac{1}{7}$ and $I ^{\text{st }}$ quadrant

Answer 1

Answer: (A)

$\cot \alpha=1, \sec \beta=\frac{-5}{3}, \cos \beta=\frac{-3}{5}, \tan \beta=\frac{-4}{3}$
$\tan (\alpha+\beta)=\frac{1-\frac{4}{3}}{1+\frac{4}{3} \times 1}=\frac{-1}{7}$