If -2 and - then tan - equal to

The correct option is B tanβ + 2tanγα + β = π2 ⇒α = π2 β ⇒tanα = β ⇒tanαtanβ = 1 ...(1) Again, β + γ = α ⇒γ = α β ⇒tanγ = tanα tanβ1+tanαtanβ ⇒tanγ = ...

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Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

If α+β=π/2 an...

Question

If $α + β = \frac{π}{2}$ and $β + γ = α,$ then tan $α$ equal to

2 (tan β + tan γ)

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tan β + tan γ

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tan β + 2 tan γ

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2 tan β + tan γ

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Solution

The correct option is C $tan β + 2 tan γ$
$α + β = \frac{π}{2}$
$\Rightarrow α = \frac{π}{2} - β$
$\Rightarrow tan α = cot β$
$\Rightarrow tan α tan β = 1 . . . (1)$

Again, $β + γ = α$
$\Rightarrow γ = α - β$
$\Rightarrow tan γ = \frac{tan α - tan β}{1 + tan α tan β}$
$\Rightarrow tan γ = \frac{tan α - tan β}{2} [from eq. (1)]$
$\Rightarrow tan α = tan β + 2 tan γ$

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Trigonometric Ratios of Multiples of an Angle

Standard XII Mathematics

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If α+β=π2 and β+γ=α, then tan α equal to

The correct option is C tanβ+2tanγα+β=π2 ⇒α=π2−β ⇒tanα=cotβ ⇒tanαtanβ=1 ...(1) Again, β+γ=α ⇒γ=α−β ⇒tanγ=tanα−tanβ1+tanαtanβ ⇒tanγ=tanα−tanβ2 [from eq. (1)] ⇒tanα=tanβ+2tanγ

If $α + β = \frac{π}{2}$ and $β + γ = α,$ then tan $α$ equal to