Find ` (dy)/(dx) , " if x " = 2 cos theta - cos 2 theta ` and
y = 2sin theta - sin 2 theta `.

Options

A. `tan""(3 theta )/(2)`
B. `- tan""(3 theta )/(2)`
C. `cot""(3 theta )/(2)`
D. `-cot""(3 theta)/(2)`

Answer

A

Explanation

Given `x=2 cos theta - cos 2 theta `
and `y= 2 sin theta- sin 2 theta `
`(dy)/(d theta )=- 2 sin theta + 2 sin 2 theta `
and `(dy)/(d theta)=(2 cos theta - 2 cos 2 theta )/(-2 sin theta + 2 sin 2 theta )`
`=( cos theta - cos 2 theata )/( sin 2 theta - sin theta )`
`=( 2 sin""((theta+ 2 theta )/(2)) sin ""((2 theta - theta)/( 2)))/( 2 cos ""((theta+ 2cos theta )/(2)) sin""((2 theta -theta )/(2)))`
`=tan""(3 theta )/(2)`