For , (0, 2 ), let 3 ( + )=2 ( - ) and a real number k be such th… - Vidyadip

MCQ

For $\alpha, \beta \in\left(0, \frac{\pi}{2}\right)$, let $3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)$ and a real number $k$ be such that $\tan \alpha=k \tan \beta$. Then the value of $\mathrm{k}$ is equal to :

A
$-\frac{2}{3}$
✓
$-5$
C
$\frac{2}{3}$
D
$ 5$

✓

Answer

Correct option: B.

$-5$

b
$3\sin \alpha \cos \beta+3 \sin \beta \cos \alpha$
$=2 \sin \alpha \cos \beta-2 \sin \beta \cos \alpha$
$5 \sin \beta \cos \alpha=-\sin \alpha \cos \beta$
$\tan \beta=-\frac{1}{5} \tan \alpha $
$\tan \alpha=-5 \tan \beta$
Not possible as $\tan \alpha, \tan \beta$ are positive
$\Rightarrow$ Data inconsistent

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