If 2 sin α cos β sin γ= sin β sin (α+γ) then tan α, tan β, tan γ are in

Question

If 2 sin α cos β sin &gamma;= sin β sin (α+&gamma;) then tan α, tan β, tan &gamma; are in (A) A.P (B) G.P. (C) H.P. (D) None of these

Tardigrade Admin · Accepted Answer

2 sin α cos β sin &gamma;= sin β sin (α+&gamma;) = sin β( sin α cos &gamma;+ cos α sin &gamma;) on dividing by sin α sin β sin &gamma;, we get 2 cot β= cot &gamma;+ cot α ⇒ (2/ tan β)=(1/ tan &gamma;)+(1/ tan &gamma;) Hence, tan α, tan β, tan &gamma; are in H.P.

Q. If $2 sin α cos β sin γ = sin β sin (α + γ)$ then $tan α, tan β, tan γ$ are in

A.P

G.P.

H.P.

None of these

$2 sin α cos β sin γ = sin β sin (α + γ)$
$= sin β (sin α cos γ + cos α sin γ)$
on dividing by $sin α sin β sin γ$ , we get
$2 cot β = cot γ + cot α$
$\Rightarrow \frac{2}{t a n β} = \frac{1}{t a n γ} + \frac{1}{t a n γ}$
Hence, $tan α, tan β, tan γ$ are in $H . P$ .

Q. If 2sinαcosβsinγ=sinβsin(α+γ) then tanα,tanβ,tanγ are in

A.P

G.P.

H.P.

None of these

2sinαcosβsinγ=sinβsin(α+γ) =sinβ(sinαcosγ+cosαsinγ) on dividing by sinαsinβsinγ, we get 2cotβ=cotγ+cotα ⇒tanβ2​=tanγ1​+tanγ1​ Hence, tanα,tanβ,tanγ are in H.P.

Q. If $2 sin α cos β sin γ = sin β sin (α + γ)$ then $tan α, tan β, tan γ$ are in

$2 sin α cos β sin γ = sin β sin (α + γ)$
$= sin β (sin α cos γ + cos α sin γ)$
on dividing by $sin α sin β sin γ$ , we get
$2 cot β = cot γ + cot α$
$\Rightarrow \frac{2}{t a n β} = \frac{1}{t a n γ} + \frac{1}{t a n γ}$
Hence, $tan α, tan β, tan γ$ are in $H . P$ .