JEE Main 2016MathematicsApplication of DerivativesMediumMCQ

JEE Main 2016 — Application of Derivatives Question with Solution

JEE Main 2016 (03 Apr)

Question

Consider fx=tan-1⁡1+sin⁡x1-sin⁡x, x ∈0,π2. A normal to y=fx at x=π6 also passes through the point

Choose an option

Show full solutionCorrect option: D
Correct answer
D0,2π3

Step-by-step explanation

fx=tan-1⁡1+sin⁡x1-sin⁡x, x ∈0,π2

f′(x)= 11+1+sin⁡x1-sin⁡x .12 1+sin⁡x1-sin⁡x-12 . cos⁡x1-sin⁡x+cos⁡1+sin⁡x1-sin⁡x2

at x=π6

f′x=122 .12 13 314=12

Slope of tangent =12

So slope of normal = -2

Also at x=π6,  y=tan-1⁡3=π3 .

So equation of the Normal would be y-π3= -2 x-π6

It passes through 0,2π3

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About this question

This is a previous-year question from JEE Main 2016, covering the Application of Derivatives 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.