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JEE Main 201322 AprilOnline
Exam
JEE Main
Year
2013
Date
22 April
Mode
Online
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2013 · 22 April · Online · Mathematics · Trigonometric Equations

The number of solutions of the equation, ^ -1 x=2 ^ -1 x (in...

The number of solutions of the equation, sin⁡−1x=2tan⁡−1x\sin ^{-1} x=2 \tan ^{-1} x (in principal values) is :

Options

  1. A1
  2. B4
  3. C2
  4. D3

Correct answer

A. 1

Step-by-step solution

Given equation is \sin ^{-1} x=2 \tan ^{-1} x Now, this equation has only one solution. ∴ LHS =sin⁡−11=π2 and  RHS =2tan⁡−11=2×π4=π2\begin{aligned}& \therefore \quad \text{ LHS }=\sin ^{-1}1=\frac{\pi}{2}\\ & \text{ and } \text{ RHS }=2 \tan ^{-1} 1=2 \times \frac{\pi}{4}=\frac{\pi}{2} \end{aligned}Also, x=1x=1 gives angle value as π4and5π45π4\frac{\pi}{4} and \frac{5 \pi}{4}\frac{5 \pi}{4} is outside the principal value.
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