Question

please help with this :​

Answer 1

Answer:

$\cos(12 \alpha ) + i \sin(12 \alpha )$

Step-by-step explanation:

$\frac{ ({\cos( \alpha ) + i \sin( \alpha ))}^{8} }{( {\sin( \alpha ) - i \cos( \alpha ))}^{4} } \: \: \: \: = \: \: \: \: \frac{ \cos(8 \alpha ) + i \sin(8 \alpha ) }{ {(i( \cos( \alpha ) - i \sin( \alpha ) ))}^{4} } \: \: \: \: \: \: = \: \: \: \: \: \: \frac{ \cos(8 \alpha ) + i \sin(8 \alpha ) }{ \cos(4 \alpha ) - i \sin(4 \alpha ) } \\ \\ \\ \\ = \frac{ \cos(8 \alpha + 4 \alpha ) + i \sin(8 \alpha + 4 \alpha ) }{1} \\ \\ \\ \\ = \cos(12\alpha ) + i \sin(12 \alpha )$