If -2 and - y - then tan - equalsA- 2tan-tan-B- tan-tan-C- tan-2 tan-D- 2 tan-tan-

The correct option is C α+β=π/2⇒ tan β=cot α tan(β+γ)=tan α⇒ tan α=tan β+tan γ/1 tan β tan γ ⇒ tan α=cot α+tan γ/1 cot α tan γ ⇒ tan α tan γ = cot α+tan γ ⇒ t ...

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Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

If α+β=π/2 an...

Question

$I f α + β = \frac{π}{2} a n d β + γ = α, t h e n t a n α e q u a l s$

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Solution

The correct option is C
$α + β = \frac{π}{2} \Rightarrow t a n β = c o t α t a n (β + γ) = t a n α \Rightarrow t a n α = \frac{t a n β + t a n γ}{1 - t a n β t a n γ} \Rightarrow t a n α = \frac{c o t α + t a n γ}{1 - c o t α t a n γ} \Rightarrow t a n α - t a n γ = c o t α + t a n γ \Rightarrow t a n α = t a n β + 2 t a n γ$

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If α+β=π2 and β+γ=α, then tan α equals

The correct option is C α+β=π2⇒tan β=cot αtan(β+γ)=tan α⇒ tan α=tan β+tan γ1−tan β tan γ⇒ tan α=cot α+tan γ1−cot α tan γ⇒tan α−tan γ=cot α+tan γ⇒tan α=tan β+2 tan γ

$I f α + β = \frac{π}{2} a n d β + γ = α, t h e n t a n α e q u a l s$