If - - Y are three angles given by -2 tan -1-2-1- -3 sin -11-2-sin -1-1-2 and Y -cos -11-3- thenA- Y-B- -C- -Y-D- -

The correct option is C β gt; γ gt; αα =2 tan^ 1 (√(2) 1) = 2 ×π/8 = π/4 = cos^ 1 (1/√(2)) β = 3 ×π/4 π/6 = 7 π/12 ∴β gt; α, Also 1/3 lt; 1/√(2)⇒ c ...

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Byju's Answer

Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

If α, β, Y ar...

Question

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

γ > β > α

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α > γ > β >

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β > γ > α

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γ > α > β

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Solution

The correct option is C $β > γ > α$
$α = 2 t a n^{- 1} (\sqrt{2} - 1) = 2 \times \frac{π}{8} = \frac{π}{4} = c o s^{- 1} (\frac{1}{\sqrt{2}}) β = 3 \times \frac{π}{4} - \frac{π}{6} = \frac{7 π}{12} ∴ β > α, A l s o \frac{1}{3} < \frac{1}{\sqrt{2}} \Rightarrow c o s^{- 1} (\frac{1}{3}) > c o s^{- 1} (\frac{1}{\sqrt{2}}) S o, γ > α A l s o β > γ$

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Similar questions

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

Q. If the coefficient of the middle term in the expansion of

(1 + x)^{2 n + 2}

α

and the coefficients of middle terms in the expansion of

(1 + x)^{2 n + 1}

are

β

and

γ

, then relation between

α, β

and

γ

is-

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. If

α, β, γ

are roots of equation

x^{3} - x - 1 = 0

, then the equation whose roots are

\frac{1}{β + γ}, \frac{1}{γ + α}, \frac{1}{α + β}

is -

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 $α$ , $β$ , & $γ$ .

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If α,β,γ are three angles given by α=2tan−1(√2−1),β=3 sin−11√2+sin−1(−12)and γ=cos−1(13), then

The correct option is C β>γ>αα=2tan−1(√2−1)=2×π8=π4=cos−1(1√2)β=3×π4−π6=7π12∴β>α,Also13<1√2⇒cos−1(13)>cos−1(1√2)So,γ>αAlso β>γ

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