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Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesAddition, Multiplication, Subtraction formula based,Multiple/Submultiple anglesMedium2 minPYQ_2024

MathematicsMediumsingle choice

For $α, β \in (0, \frac{π}{2})$ let $3 \sin (α + β) = 2 \sin (α - β)$ and a real number $k$ be such that $\tan α = \tan β$ . Then the value of $k$ is equal to

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Answer:

Solution:

Given:
$3 \sin (α + β) = 2 \sin (α - β)$
$\Rightarrow \frac{\sin (α + β)}{\sin (α - β)} = \frac{2}{3}$
$\Rightarrow \frac{\sin (α + β) + \sin (α - β)}{\sin (α + β) - \sin (α - β)} = \frac{2 + 3}{2 - 3}$
$\Rightarrow \frac{2 \sin α \cos β}{2 \cos α \sin β} = - 5$
$\Rightarrow \frac{\tan α}{\tan β} = - 5$
$\Rightarrow \tan α = - 5 \tan β$
$\Rightarrow k = - 5$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Addition, Multiplication, Subtraction formula based,Multiple/Submultiple angles

⏱ 2mℹ️ Source: PYQ_2024

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