- and - are the positive acute angles and satisfying equations 5sin 2- - 3sin 2- and tan- - 3tan- simultaneously- Then the value of tan- -tan- is

If $α, β ϵ (0, \frac{π}{2})$ satisfy the following simultaneous equation $2 s i n 2 β = 3 s i n 2 α a n d t a n β = 3 t a n α$ , then the value of ( $8 c o s 2 α)$ is ___

Q. Let

α, β

are acute and

tan α = \frac{a}{a + 1}

tan β = \frac{1}{2 a + 1}

, then find the value of

α + β

Q. If

α

and

β

are acute angle such that

tan α = \frac{m}{m + 1}

and

tan β = \frac{1}{2 m + 1}

. Then find m if

α + β = \frac{π}{m}

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α and β are the positive acute angles and satisfying equations 5sin2β=3sin2α and tanβ=3tanα simultaneously. Then the value of tanα+tanβ is

Given tanβ=3tanαAlso given 5sin2β=3sin2α⇒5(2tanβ1+tan2β)=3(2tanα1+tan2α)⇒30tanα1+9tan2α=6tanα1+tan2α⇒24tanα−24tan3α=0⇒tanα=−1,0,1Since,α,β are positive acute angles tanα=1⇒tanβ=3⇒tanα+tanβ=4

$α$ and $β$ are the positive acute angles and satisfying equations $5 sin 2 β = 3 sin 2 α$ and $tan β = 3 tan α$ simultaneously. Then the value of $tan α + tan β$ is