If cot - - -2- cot - cot - - -2 from G-P- for all permissible values of - - - then cos - in terms of the trigonometric ratios of - and - can be expressed as

The correct option is C cos β cos 2 γ Given nbsp; cot^2γ = cot α+β2 . nbsp;cot α β2 ⇒ nbsp;cos^2γsin^2γ = cos nbsp;α+β2 . nbsp;cos ...

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Standard XII

Mathematics

Theorems for Continuity

If cot α - ...

Question

If $c o t (\frac{α - β}{2}), c o t γ, c o t (\frac{α + β}{2})$ from G.P. for all permissible values of $α, β, γ$ then $c o s α$ in terms of the trigonometric ratios of $β$ and $γ$ can be expressed as

c o s β s i n 2 γ

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c o s β c o s 2 γ

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c o s 2 β c o s γ

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s i n β s i n 2 γ

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Solution

The correct option is C $c o s β c o s 2 γ$
Given
$c o t^{2} γ = c o t \frac{α + β}{2} . c o t \frac{α - β}{2}$
$\Rightarrow \frac{c o s^{2} γ}{s i n^{2} γ} = \frac{c o s \frac{α + β}{2} . c o s \frac{α - β}{2}}{s i n \frac{α + β}{2} . s i n \frac{α - β}{2}}$
Applying componendo and dividendo
$\frac{1}{c o s^{2} γ - s i n^{2} γ} = \frac{c o s \frac{α + β}{2} . c o s \frac{α - β}{2} + s i n \frac{α + β}{2} . s i n \frac{α - β}{2}}{c o s \frac{α + β}{2} . c o s \frac{α - β}{2} - s i n \frac{α + β}{2} . s i n \frac{α - β}{2}}$
$\Rightarrow \frac{1}{c o s 2 γ} = \frac{c o s β}{c o s α}$
$∴ c o s α = c o s β . c o s 2 γ$
Option B is correct.

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Similar questions

cos (α + β + γ) + cos (α - β - γ) + cos (β - γ - α) + cos (γ - α - β) =

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Q. If

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In each of $α$ $β$ and $γ$ $is a positive acute angle such that$
$sin (α + β - γ) = \frac{1}{2}, cos (β + γ - α) = \frac{1}{2} and tan (γ + α - β) = 1$
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Q. If

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If cot(α−β2),cotγ,cot(α+β2) from G.P. for all permissible values of α,β,γ then cosα in terms of the trigonometric ratios of β and γ can be expressed as

If $c o t (\frac{α - β}{2}), c o t γ, c o t (\frac{α + β}{2})$ from G.P. for all permissible values of $α, β, γ$ then $c o s α$ in terms of the trigonometric ratios of $β$ and $γ$ can be expressed as