JEE Main 2021MathematicsDifferentiationMediumMCQ

JEE Main 2021 — Differentiation Question with Solution

JEE Main 2021 (27 Aug Shift 2)

Question

If y(x)=cot-11+sinx+1-sinx1+sinx-1-sinx, x∈π2,π, then dydx at x=5π6 is:

Choose an option

Show full solutionCorrect option: C
Correct answer
C-12

Step-by-step explanation

y(x)=cot−1⁡1+sin⁡x+1−sin⁡x1+sin⁡x−1−sin⁡x

As we know that, 1-sin⁡x =sinx2- cosx2 & 1+sin⁡x =sinx2+ cosx2

y(x)=cot−1⁡cos⁡x2+sin⁡x2+cos⁡x2−sin⁡x2cos⁡x2+sin⁡x2−cos⁡x2−sin⁡x2

=cot−1⁡cos⁡x2+sin⁡x2+sin⁡x2−cos⁡x2cos⁡x2+sin⁡x2−sin⁡x2+cos⁡x2 for x∈π2,π

=cot−1⁡sin⁡x2cos⁡x2

=cot−1⁡tan⁡x2

=cot−1⁡cot⁡(π2-x2)

y(x)=π2−x2

y′(x)=−12

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About this question

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