JEE Main 2021MathematicsTrigonometric EquationsMediumMCQ

JEE Main 2021 — Trigonometric Equations Question with Solution

JEE Main 2021 (25 Jul Shift 2)

Question

The number of distinct real roots of sinxcosxcosxcosxsinxcosxcosxcosxsinx=0 in the interval -π4≤x≤π4 is:

Choose an option

Show full solutionCorrect option: B
Correct answer
B1

Step-by-step explanation

We have, sinxcosxcosxcosxsinxcosxcosxcosxsinx=0,-π4≤x≤π4

Apply: R1→R1-R2 and R2→R2-R3

sinx-cosxcosx-sinx00sinx-cosxcosx-sinxcosxcosxsinx=0

⇒sinx-cosx21-1001-1cosxcosxsinx=0

⇒sinx-cosx2sinx+2cosx=0

⇒sinx=cosx or sinx=-2cosx

∴ x=π4

Since, -π4≤x≤π4, we get -1≤tanx≤1

⇒tanx=1⇒x=π4

Hence, number of roots is one.

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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.