JEE Main 2021MathematicsInverse Trigonometric FunctionsMediumMCQ

JEE Main 2021 — Inverse Trigonometric Functions Question with Solution

JEE Main 2021 (17 Mar Shift 1)

Question

The sum of possible values of x for tan-1x+1+cot-11x-1=tan-1831 is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A-324

Step-by-step explanation

Given tan-1x+1+cot-11x-1=tan-1831

⇒tan-1x+1+tan-1x-1=tan-1831,   ∴tan-1x=cot-11x, x>0

⇒tan-1x+1+x-11-x+1x-1=tan-1831

⇒tan-12x1-x+1x-1=tan-1831

Taking tangent both the sides we get, 

(x+1)+(x-1)1-x2-1=831

⇒2x2-x2=831

⇒4x2+31x-8=0

⇒x=-8,14

But, if x=14

tan-1x+1∈0,π2

and cot-11x-1∈π2,π

⇒LHS>π2 and RHS<π2 (Not possible)

Hence, x=-8=-324. 

 

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About this question

This is a previous-year question from JEE Main 2021, covering the Inverse Trigonometric Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.