If cot α=1 and sec β=-(5/3), where π

Question

If cot α=1 and sec β=-(5/3), where π<α<(3 π/2) and (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 IV text th quadrant (B) 7 and I text st quadrant (C) -7 and IV text th quadrant (D) (1/7) and I textst quadrant

Tardigrade Admin · Accepted Answer

cot α=1, sec β=(-5/3), cos β=(-3/5), tan β=(-4/3) tan (α+β)=(1-(4/3)/1+(4)3 × 1)=(-1/7)

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

$- \frac{1}{7}$ and $I V^{th}$ quadrant

7 and $I^{st}$ quadrant

$- 7$ and $I V^{th}$ quadrant

$\frac{1}{7}$ and $I^{st}$ quadrant

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

Q. If cotα=1 and secβ=−35​, where π<α<23π​ and 2π​<β<π, then the value of tan(α+β) and the quadrant in which α+β lies, respectively are

−71​ and IV th quadrant

7 and Ist quadrant

−7 and IVth quadrant

71​ and Ist quadrant