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$\large\frac{(cosx+isinx)(cosy+isiny)}{(cotu+i)(1+itanv)}=?$

(A) $=(sinv.cosu)(cos(x+y-u-v)+isin(x+y-u-v)$

(B) $=(sinu.cosv)(cos(x+y-u-v)+isin(x+y-u-v)$

(C) $=(sinu.cosv)(cos(x+y-u-v)-isin(x+y-u-v)$

(D) $=(sinv.cosu)(cos(x+y-u-v)-isin(x+y-u-v)$

Can you answer this question?
 
 

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Toolbox:
  • $r(cos\theta+isin\theta)=r\:cis\theta$
  • If $z_1=cis\theta_1\:\:and\:\:z_2=cis\theta$, then $z_1.z_2=cis(\theta_1+\theta_2)\:\:and\:\:\large\frac{z_1}{z_2}=$$cis(\theta_1-\theta_2)$
$\large\frac{(cosx+isinx)(cosy+isiny)}{(cotu+i)(1+itanv)}$
$=\large\frac{(sin u cosv)(cosx+isinx)(cosy+isiny)}{(cosu+isinu)(cosv+isinv)}$
$=(sinu.cosv)(cos(x+y-u-v)+isin(x+y-u-v)$
answered Jul 31, 2013 by rvidyagovindarajan_1
 

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