For α,β∈0,(π)/2 let 3sin(α+β)=2sin(α-β) and a real number k be such that tanα= tanβ. Then the value of k is equal to

Question

MARKS Content Team · Accepted Answer

Correct answer: (A) -5. Given: 3sinα+β=2sinα-β ⇒(sinα+β)/(sinα-β)=2/3 ⇒(sinα+β+sinα-β)/(sinα+β-sinα-β)=(2+3)/(2-3) ⇒(2sinαcosβ)/(2cosαsinβ)=-5 ⇒(tanα)/(tanβ)=-5 ⇒tanα=-5tanβ ⇒k=-5

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

Solution

Relevant Questions

For α,β∈0,π2 let 3sin(α+β)=2sin(α-β) and a real number k be such that tanα= tanβ. Then the value of k is equal to

Solution

Relevant Questions

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