- - and -are three angles given by - - 2tan -1 -2-1 - - 3sin -11-2-sin -1 -12 and - - cos -113- Then

The correct options are A β > γ C α α= 2tan^ 1( √(2) 1 ) ⇒tan α #160; 2 =√( 2 ) 1 tan α = 2(√( 2 ) 1) / 1 (√( 2 ) 1)^ 2 #160 ...

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Byju's Answer

Standard XII

Mathematics

Perpendicular Distance of a Point from a Line

α, β and γa...

Question

$α, β$ and $γ$ are three angles given by $α = 2 {tan}^{- 1} (\sqrt{2} - 1), β = 3 {sin}^{- 1} \frac{1}{\sqrt{2}} + {sin}^{- 1} (- \frac{1}{2})$ and $γ = {cos}^{- 1} \frac{1}{3} .$ Then

α > β

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β > γ

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α < γ

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α > γ

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Solution

The correct options are
A $β > γ$
C $α < γ$
$α = 2 {tan}^{- 1} (\sqrt{2} - 1)$
$\Rightarrow tan \frac{α}{2} = \sqrt{2} - 1$
$tan α = \frac{2 (\sqrt{2} - 1)}{1 - (\sqrt{2} - 1)^{2}} = 1$
$\Rightarrow α = \frac{π}{4}$
$β = 3 {sin}^{- 1} \frac{1}{\sqrt{2}} + {sin}^{- 1} (- \frac{1}{2})$
$\Rightarrow β = \frac{3 π}{4} - \frac{π}{6} = \frac{7 π}{12}$
$γ = {cos}^{- 1} \frac{1}{3} .$

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Similar questions

Q. If

α, β, γ

are three angles given by

α = 2 t a n^{- 1} (\sqrt{2} - 1), β = 3 s i n^{- 1} \frac{1}{\sqrt{2}} + s i n^{- 1} (\frac{- 1}{2}) a n d γ = c o s^{- 1} (\frac{1}{3}),

then

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

Q. If each of

α, β, 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

, find the value of

α, β, γ

Q. Let

α, β, γ

be three numbers such that

\frac{1}{α} + \frac{1}{β} + \frac{1}{γ} = \frac{1}{2}, \frac{1}{α^{2}} + \frac{1}{β^{2}} + \frac{1}{γ^{2}} = \frac{9}{4}

and

α + β + γ = 2

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Q. Find a cubic polynomial whose zeros are

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and

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such that

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and

α β γ = - 6

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α,β and γare three angles given by α=2tan−1(√2−1),β=3sin−11√2+sin−1(−12) and γ=cos−113. Then

The correct options are A β>γ C α<γα=2tan−1(√2−1)⇒tanα2=√2−1tanα=2(√2−1)1−(√2−1)2=1⇒α=π4β=3sin−11√2+sin−1(−12) ⇒β=3π4−π6=7π12γ=cos−113.

$α, β$ and $γ$ are three angles given by $α = 2 {tan}^{- 1} (\sqrt{2} - 1), β = 3 {sin}^{- 1} \frac{1}{\sqrt{2}} + {sin}^{- 1} (- \frac{1}{2})$ and $γ = {cos}^{- 1} \frac{1}{3} .$ Then