logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
0 votes

If $ \large\frac{3}{2+cos\theta+isin\theta}=$$x+iy$, then $ (x-1)(x-3)=?$

(A) $y^2$

(B) $-y^2$

(C) $0$

(D) $1$

Can you answer this question?
 
 

1 Answer

0 votes
Given: $x+iy=\large\frac{3}{2+cos\theta+isin\theta}$
By rationalising the denominator we get
$\Rightarrow\:x+iy=\large\frac{3[(2+cos\theta)-isin\theta]}{(2+cos\theta)^2+sin^2\theta}$
$=\large\frac{3(2+cos\theta)-i(3sin\theta)}{5+4cos\theta}$
$\Rightarrow\:x=\large\frac{3(2+cos\theta)}{5+4cos\theta}$ $and\:\:y=\large\frac{-3sin\theta}{5+4cos\theta}$
$\Rightarrow\:(x-1)(x-3)=\large\frac{(1-cos\theta)}{5+4cos\theta}.\frac{-9(1+cos\theta)}{5+4cos\theta}$
$=\large\frac{-9sin^2\theta}{(5+4cos\theta)^2}$$=-y^2$
answered Jul 31, 2013 by rvidyagovindarajan_1
edited May 26, 2014 by rohanmaheshwari0831_1
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...