Question

great opportunity for points and a thanks and a brainleast​

Answer 1

Answer:

$tan \frac{ \alpha }{2} = \frac{1 - {tan}^{2} \frac{ \alpha }{2} }{2tan \frac{ \alpha }{2} } - \frac{2tan \frac{ \alpha }{2} }{1 - {tan}^{2} \frac{ \alpha }{2} } =$

$tan \frac{ \alpha }{2} = \frac{1 + {tan}^{4} \frac{ \alpha }{2} -2 tan \frac{ \alpha }{2} - 4tan \frac{ \alpha }{2}}{2tan \frac{ \alpha }{2} - 2 {tan}^{2} \frac{ \alpha }{2} }$

$2 {tan}^{2} \frac{ \alpha }{2} - 2 {tan}^{3} \frac{ \alpha }{2} = 1 + {tan}^{4} \frac{ \alpha }{2} - 6 {tan} \frac{ \alpha }{2}$

${tan}^{4} \frac{ \alpha }{2} + 2 {tan}^{3} \frac{ \alpha }{2} - 2 {tan}^{2} \frac{ \alpha }{2} - 6tan \frac{ \alpha }{2} + 1 = 0$