Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Prove the following: 1. 3 sin inverse x = sin inverse (3x - 4x ^ 3), x belongs to [- 1 / 2, 1 / 2]

Prove the following:

    1. 3\sin^{-1}x = \sin^{-1}(3x - 4x^3),\;\;x\in\left[-\frac{1}{2},\frac{1}{2} \right ]

Answers (1)

best_answer

Given to prove: 3\sin^{-1}x = \sin^{-1}(3x - 4x^3) 

    where,     x\:\epsilon \left[-\frac{1}{2},\frac{1}{2} \right ].

Take \theta= \sin ^{-1}x  or   x = \sin \theta

Take R.H.S value  

\sin^{-1}(3x - 4x^3)

= \sin^{-1}(3\sin \theta - 4\sin^3 \theta)

= \sin^{-1}(\sin 3\theta)                                        \left ( \because 3\sin \theta - 4\sin^3 \theta \right = \sin 3 \theta )

= 3\theta

= 3\sin^{-1}x   =   L.H.S

Posted by

Divya Prakash Singh

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE practical exams 2026 will be cancelled over non-compliance with guidelines, says board

Latest Question