If 2y=\left ( \cot ^{-1}\left ( \frac{\sqrt{3}\cos x+\sin x}{\cos x-\sqrt{3}\sin x} \right ) \right )^{2},x\; \epsilon \left ( 0,\frac{\pi}{2} \right ) then \frac{dy}{dx} is equal to :


 

  • Option 1)

    \frac{\pi }{6}-x

  • Option 2)

    \frac{\pi }{3}-x

  • Option 3)

    x-\frac{\pi }{6}

     

  • Option 4)

    2x-\frac{\pi }{3}

 

Answers (1)

2y=\left ( \cot ^{-1}\left ( \frac{\sqrt{3}\cos x+\sin x}{\cos x-\sqrt{3}\sin x} \right ) \right )^{2} \; \; \; \; \; \; x\; \epsilon \left ( 0, \frac{\pi }{2}\right )

then \frac{dy}{dx},

2y=\left ( \cot ^{-1}\left ( \frac{\frac{\sqrt{3}\cos x}{\cos x}+\frac{\sin x}{\cos x}}{\frac{\cos x}{\cos x}-\frac{\sqrt{3}\sin x}{\cos x}} \right ) \right )^{2}

=\left ( \cot ^{-1}\left ( \frac{\sqrt{3}+\tan x}{1-\sqrt{3}\tan x} \right ) \right )^{2}

=\left ( \cot ^{-1}\left ( \tan \left ( \frac{\pi}{3}+x \right ) \right ) \right )^{2}

=\left ( \frac{\pi}{2}-\tan ^{-1}\left ( \tan \left ( \frac{\pi}{3}+x \right ) \right ) \right )^{2}

=\left ( \frac{\pi}{2}-\left ( \frac{\pi}{3}+x \right ) \right )^{2}

= \left ( \frac{\pi}{2}-\frac{\pi}{3}-x \right )^{2}=\left ( \frac{\pi}{6}-x \right )^{2}

2y=\left ( x-\frac{\pi}{6} \right )^{2}

\frac{dy}{dx}=\frac{1}{2}\times2\left ( x-\frac{\pi}{6} \right )

=x-\frac{\pi}{6}


Option 1)

\frac{\pi }{6}-x

Option 2)

\frac{\pi }{3}-x

Option 3)

x-\frac{\pi }{6}

 

Option 4)

2x-\frac{\pi }{3}

Preparation Products

Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Test Series JEE Main April 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Test Series JEE Main April 2022

Take chapter-wise, subject-wise and Complete syllabus mock tests and get an in-depth analysis of your test..

₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions