The number of integers for which the equation ^ -1 x + ^ -1 x + ^ -1 x = n has real solution(s) is

Correct answer: C. 2 Given equation is& (π)/(2) + ^ - 1 x = n, x ∈ [ - 1, 1 ] Now LHS ∈ [(π)/(4), (3π)/(4)] Integers in this interval are 1 & 2 Hence, there are~ 2 & integers for which the equation has real solutions

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

The number of integers for which the equation ^ -1 x + ^ -1 x + ^...

The number of integers for which the equation

\sin^{-1} x + \cos^{-1} x + \tan^{-1} x = n

has real solution(s) is

Options

A $0$
B $1$
C $2$
D $3$

Correct answer

C. $2$

Step-by-step solution

Given equation is& $\dfrac{π}{2} + \tan^{- 1} x = n, \forall x \in [ - 1, 1 ]$
Now LHS ∈ \left[\dfrac{π}{4}, \dfrac{3\pi}{4}\right] $<br />Integers in this interval are$ 1 & 2 $</p><p>Hence, there are~$ 2$& integers for which the equation has real solutions

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