If tan-2 sin- - sin- - cosec- then - - - are in

The correct option is A A.P.tanβ = 2sinα . sinγ . cos ec( α + γ) = 2sinαsinγ/sin( α + γ) β = sin( α + γ)/2sinαsinγ i.e. 2β = sinαcosγ + cosαsinγ/sinαsinγ = α ...

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Standard XI

Mathematics

Sin(A+B)Sin(A-B)

If tanβ=2 sin...

Question

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

A.P.

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G.P.

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H.P.

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none of these

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Solution

The correct option is A A.P.
$tan β = 2 sin α . sin γ . cos e c (α + γ) = \frac{2 sin α sin γ}{sin (α + γ)}$
$cot β = \frac{sin (α + γ)}{2 sin α sin γ}$
i.e. $2 cot β = \frac{sin α cos γ + cos α sin γ}{sin α sin γ} = cot α + cot γ$

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If tanβ=2sinα.sinγ.cosec(α+γ), then cotα,cotβ,cotγ are in

The correct option is A A.P.tanβ=2sinα.sinγ.cosec(α+γ)=2sinαsinγsin(α+γ) cotβ=sin(α+γ)2sinαsinγ i.e. 2cotβ=sinαcosγ+cosαsinγsinαsinγ=cotα+cotγ

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

The correct option is A A.P.
$tan β = 2 sin α . sin γ . cos e c (α + γ) = \frac{2 sin α sin γ}{sin (α + γ)}$
$cot β = \frac{sin (α + γ)}{2 sin α sin γ}$
i.e. $2 cot β = \frac{sin α cos γ + cos α sin γ}{sin α sin γ} = cot α + cot γ$