Last updated at May 12, 2021 by Teachoo

Transcript

Misc 15 sin(tanβ1 x), |π₯| < 1 is equal to (A) π₯/β(1 β π₯2) (B) 1/β(1 β π₯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) We convert tanβ1 to sinβ1 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(γ1 + π₯γ^2 )) Now solving sin(tanβ1 x) = sin (a) = sin ("sinβ1 " (π/β(γπ + πγ^π ))) = π₯/β(γ1 + π₯γ^2 ) Hence, D is the correct answer

Miscellaneous

Misc. 1

Misc. 2 Important

Misc. 3 Deleted for CBSE Board 2021 Exams only

Misc. 4 Important Deleted for CBSE Board 2021 Exams only

Misc. 5 Deleted for CBSE Board 2021 Exams only

Misc. 6 Deleted for CBSE Board 2021 Exams only

Misc. 7 Important Deleted for CBSE Board 2021 Exams only

Misc. 8 Important Deleted for CBSE Board 2021 Exams only

Misc. 9 Important Deleted for CBSE Board 2021 Exams only

Misc. 10 Important Deleted for CBSE Board 2021 Exams only

Misc. 11 Important Deleted for CBSE Board 2021 Exams only

Misc 12 Important Deleted for CBSE Board 2021 Exams only

Misc. 13 Important Deleted for CBSE Board 2021 Exams only

Misc. 14 Deleted for CBSE Board 2021 Exams only

Misc. 15 Important Deleted for CBSE Board 2021 Exams only You are here

Misc 16 Important Deleted for CBSE Board 2021 Exams only

Misc. 17 Important Deleted for CBSE Board 2021 Exams only

Chapter 2 Class 12 Inverse Trigonometric Functions

Serial order wise

About the Author

Davneet Singh

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.