logo

Ask Questions, Get Answers

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

If $a=cos\alpha+isin\alpha$, $b=cos\beta+isin\beta$, $c=cos\gamma+isin\gamma$ and $\large\frac{b}{c}+\frac{c}{a}+\frac{a}{b}$ = 1, then $cos(\beta-\gamma)+cos(\gamma-\alpha)+cos(\alpha-\beta)$ = ?

$\begin{array}{1 1}(A) \large\frac{3}{2} \\ (B) \large\frac {-3}{2} \\ (C) 0 \\(D) 1 \end{array}$

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • If $z_1=cis\theta_1\:and\:z_2=cis\theta_2$, then $\large\frac{z_1}{z_2}=$$cis(\theta_1-\theta_2)$
Given: $a=cos\alpha+isin\alpha,\:b=cos\beta+isin\beta,\:c=cos\gamma+isin\gamma$
$\Rightarrow\:\large\frac{b}{c}$$=cos(\beta-\gamma)+isin(\beta-\gamma)=cis(\beta-\gamma)$
$\large\frac{c}{a}$$=cos(\gamma-\alpha)+isin(\gamma-\alpha)=cis(\gamma-\alpha)$. and
$\large\frac{a}{b}$$=cos(\alpha-\beta)+isin(\alpha-\beta)=cis(\alpha-\beta)$
Given: $\large\frac{b}{c}+\frac{c}{a}+\frac{a}{b}$$=1$
$\Rightarrow\:cos(\beta-\gamma)+cos(\gamma-\alpha)+cos(\alpha-\beta)=1$
answered Aug 1, 2013 by rvidyagovindarajan_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
...