Find $\frac{{dy}}{{dx}},$ if $x = 2{\rm{cos\theta }} - \cos 2{\rm{\theta }}$ and $y = 2\sin {\rm{\theta }} - \sin 2{\rm{\theta }}{\rm{.}}$

$\tan \frac{{3{\rm{\theta }}}}{2}$

$ - \tan \frac{{3{\rm{\theta }}}}{2}$

$\cot \frac{{3{\rm{\theta }}}}{2}$

$ - \cot \frac{{3{\rm{\theta }}}}{2}$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

Find

\frac{{dy}}{{dx}},

x = 2\mathrm{cos\theta } - \cos 2\mathrm{\theta }

and

y = 2\sin \mathrm{\theta } - \sin 2\mathrm{\theta }\mathrm{.}

View answer and explanation

Correct option: A

\tan \frac{{3\mathrm{\theta }}}{2}

Option A (

\tan \frac{{3\theta }}{2}

) is correct because after differentiating x and y with respect to

\theta

and simplifying,

\frac{{dy}}{{dx}}

equals

\tan \frac{{3\theta }}{2}