Question

If
$cot α=1$ and $sec β=−\frac{5}{3}$ where $π<α<\frac{3π}{2} and \frac{π}{2}<β<π$
, then the value of tan(α + β) and the quadrant in which α + β lies, respectively are :

• A. -1/7 and IVth quadrant
• B. 7 and Ist quadrant
• C. – 7 and IVth quadrant
• D. 1/7 and Ist quadrant

Answer 1

Answer: (A)

-1/7 and IVth quadrant

Answer 2

The correct answer is (A) : $-\frac{1}{7}$ and IVth quadrant
∵ cot α = 1,
$α∈(π, \frac{3π}{2})$
then tan α = 1 and $sec⁡ β=−\frac{5}{3}, β∈(\frac{π}{2},π)$
then $tan⁡ β=−\frac{4}{3}$
$∴tan⁡(α+β)=\frac{tan⁡α+tan⁡β}{1−tan⁡α⋅tan⁡β}$
$=\frac{1−\frac{4}{3}}{1+\frac{4}{3}}$
$=−\frac{1}{7}$
$α+β∈(\frac{3π}{2},2π)$
i.e. fourth quadrant