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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

A

2 (tan β + tan γ)

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B

tan β + tan γ

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C

tan β + 2 tan γ

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D

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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