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 April 16, 2024 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)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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