# How do you perform the operation in trigonometric form (cos50+isin50)/(cos20+isin20)?

$\frac{1}{2} \left(i + \sqrt{3}\right)$
$\frac{\cos 50 + i \sin 50}{\cos 20 + i \sin 20} = \frac{\left(\cos 50 + i \sin 50\right) \left(\cos 20 - i \sin 20\right)}{\left(\cos 20 + i \sin 20\right) \left(\cos 20 - i \sin 20\right)} = \frac{\cos 50 \cos 20 + i \left(\sin 50 \cos 20 - \sin 20 \cos 50\right) - {i}^{2} \sin 50 \sin 20}{{\cos}^{2} 20 - {i}^{2} {\sin}^{20}} = \frac{\cos 50 \cos 20 + i \left(\sin 50 \cos 20 - \sin 20 \cos 50\right) + \sin 50 \sin 20}{{\cos}^{2} 20 + {\sin}^{2} 20} = \frac{\cos \left(50 - 20\right) + i \sin \left(50 - 20\right)}{1} = \cos 30 + i \sin 30 = \frac{\sqrt{3}}{2} + i \cdot \frac{1}{2} = \frac{1}{2} \left(i + \sqrt{3}\right)$since ${i}^{2} = - 1$[Ans]