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JEE Main 20179 AprilOnline
Exam
JEE Main
Year
2017
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main 2017 · 9 April · Online · Mathematics · Inverse Trigonometric Functions

A value of x satisfying the equation sin [ ^ - 1 (1 + x)] = [ ^ - 1...

A value of xx satisfying the equation sinsin\left[\cot^{- 1} \left(1 + x\right)\right] = \cos \left[\tan^{- 1} x\right], is:A value of x satisfying the equation sin [ ^ - 1 (1 + x)] = [ ^ - 1 x], is:

Options

  1. A−12- \dfrac{1}{2}
  2. B00
  3. C−1- 1
  4. D12\dfrac{1}{2}

Correct answer

A. −12- \dfrac{1}{2}

Step-by-step solution

sin⁡[cot][−1(1+x)]=cos⁡(tan)(−1x)\sin \left[cot\right]\left[- 1 ( 1 + x )\right] = \cos \left(tan\right)\left(- 1x\right)

A value of x satisfying the equation sin [ ^ - 1 (1 + x)] = [ ^ - 1 x], is:

Let, cotλ = 1 + x

tanβ = x

\to sinλ = cosβ

→1x2+2x+2=111+x2\to \dfrac{1}{\sqrt{{x}^{2} + 2x + 2}} = \dfrac{1}{1\sqrt{1 + {x}^{2}}}

→x2+2x+2=x2+1\to {x}^{2} + 2x + 2 = {x}^{2} + 1

→x=−1/2\to x = - 1 / 2

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