Question:

If $\sin (α + β) = 6 \sin (α - β)$ and $k = \frac{\tan α}{\tan β}$ , then, what is the value of $k$ ?

Updated On: Mar 28, 2026

Show Solution

Verified By Collegedunia

The Correct Option is D

Explanation:
Given,

\sin (α + β) = 6 \sin (α - β) and k = \frac{\tan α}{\tan β}

\sin (α + β) = 6 \sin (α - β)

\Rightarrow \sin α \cos β + \cos α \sin β = 6 \sin α \cos β - 6 \cos α \sin β

\Rightarrow \cos α \sin β + 6 \cos α \sin β = 6 \sin α \cos β - \sin α \cos β

\Rightarrow 7 \cos α \sin β = 5 \sin α \cos β

\Rightarrow \frac{\sin α}{\cos α} = \frac{7}{5} \times \frac{\sin β}{\cos β}

\Rightarrow tan α = \frac{7}{5} \times \tan β

\Rightarrow k = \frac{\tan α}{\tan β} = \frac{7}{5}

∴

The value of

k is \frac{7}{5}

Hence, the correct option is (D).

Was this answer helpful?