JEE Main 2021MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2021 — Trigonometric Equations Question with Solution

JEE Main 2021 (01 Sep Shift 2)

Question

If n is the number of solutions of the equation 2cosx4sinπ4+xsinπ4-x-1=1, x∈0,π and S is the sum of all these solutions, then the ordered pair n,S is :

Choose an option

Show full solutionCorrect option: B
Correct answer
B3,13π9

Step-by-step explanation

2cosx4sinπ4+xsinπ4-x-1=1

⇒  2cosx2cos2x-2cosπ2-1=1

⇒  2cosx2.2cos2x-1-1=1

⇒ 2cosx4cos2x-3=1

⇒ 4cos3x-3cosx=12

⇒ cos3x=12

⇒ 3x=π3,5π3,7π3

⇒ x=π9,5π9,7π9

No. of solutions =n=3

Sum of solutions =S=π9+5π9+7π9=13π9

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About this question

This is a previous-year question from JEE Main 2021, covering the Trigonometric Equations 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.