CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

Question 10 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Sept. 4, 2021 by Teachoo

sin (tan−1x), where |x| < 1, is equal to:

(a) x/√(1 - x
^{
2
}
) (b) 1/√(1 - x
^{
2
}
)
(c) 1/√(1 + x
^{
2
}
) (d) x/√(1 + x
^{
2
}
)

Question 10 sin (tanβ1x), where |x| < 1, is equal to: (a) π₯/β(1 β π₯^2 ) (b) 1/β(1 βγ π₯γ^2 ) (c) 1/β(1 + π₯^2 ) (d) π₯/β(1 + π₯^2 )
Let a = tanβ1 x
tan a = x
We need to find sin a.
For this first we calculate sec a and cos a
We know that
sec2 a = 1 + tan2 a
sec a = β(1+π‘ππ2 a)
sec a = β(1+π₯2)
1/cosβ‘π = β(1+π₯2)
1/β(1 + π₯^2 ) = cosβ‘π
πππβ‘π = π/β(π + π^π )
We know that
sin a = β("1 β cos2 a" )
sin a = β("1 β" (1/β(1 + π₯^2 ))^2 )
sin a = β("1 β" 1/(1 + π₯2))
sin a = β((1 + π₯2 β 1)/(1 + π₯2)) = β((π₯2 )/(1 + π₯2)) = β(π₯^2 )/β(γ1 + π₯γ^2 ) = π₯/β(γ1 + π₯γ^2 )
sin a = π₯/β(γ1 + π₯γ^2 )
a = sinβ1 (π/β(γπ + πγ^π ))
Now solving
sin(tanβ1 x)
= sin (a)
= sin ("sinβ1 " (π/β(γπ + πγ^π )))
= π₯/β(γ1 + π₯γ^2 )
So, the correct answer is (d)

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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.