If α+β=π / 2 and β+γ=α, then tan α equals

Question

If α+β=π / 2 and β+&gamma;=α, then tan α equals (A) 2( tan β+ tan &gamma;) (B)  tan β+ tan &gamma; (C)  tan β+2 tan &gamma; (D) 2 tan β+ tan &gamma;

Tardigrade Admin · Accepted Answer

α+β=(π/2) or α=(π/2)-β ⇒ tan α= cot β or tan α tan β=1 ...(i) Again, β+&gamma;=α or &gamma;=α-β ⇒ tan &gamma;=( tan α- tan β/1+ tan α tan β) =( tan α- tan β/2) [using Eq. (i)] or tan α= tan β+2 tan &gamma;

Q. If $α + β = π /2$ and $β + γ = α$ , then $tan α$ equals

$2 (tan β + tan γ)$

$tan β + tan γ$

$tan β + 2 tan γ$

$2 tan β + tan γ$

Q. If α+β=π/2 and β+γ=α, then tanα equals

2(tanβ+tanγ)

tanβ+tanγ

tanβ+2tanγ

2tanβ+tanγ

α+β=2π​ or α=2π​−β ⇒tanα=cotβ or tanαtanβ=1 ...(i) Again, β+γ=α or γ=α−β ⇒tanγ=1+tanαtanβtanα−tanβ​ =2tanα−tanβ​ [using Eq. (i)] or tanα=tanβ+2tanγ

Q. If $α + β = π /2$ and $β + γ = α$ , then $tan α$ equals

$2 (tan β + tan γ)$

$tan β + tan γ$

$tan β + 2 tan γ$

$2 tan β + tan γ$