If - - -2 and - - then tan - equals

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 ⇒ tan α = tan β + 2 tan γ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

If α+β = π/2 ...

Question

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

2 (t a n β + t a n γ)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

t a n β + t a n γ

No worries! We‘ve got your back. Try BYJU‘S free classes today!

t a n β + 2 t a n γ

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2 t a n β + t a n γ

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

Suggest Corrections

Similar questions

Q. If

α + β = \frac{π}{2}

and

β + γ = α,

then tan

α

equal to

Q. If

α + β = \frac{π}{2}

and

β + γ = α

then

tan α

equals

Q. If

α + β = \frac{π}{2}

and

β + γ = α

, then

tan α

equals-

Q. If

(α + β) = \frac{π}{2}

and

(β + γ) = α

, then

t a n α

equals

Q. If

α + β + γ = π

, then

{sin}^{2} α + {sin}^{2} β - {sin}^{2} γ

is equal to

Join BYJU'S Learning Program

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

The correct option is C tan β+2 tan γα+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

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