Browse Questions

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 $cos(\beta-\gamma)+cos(\gamma-\alpha)+cos(\alpha-\beta)$ = ?

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

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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)$