Question 6 - A-Level Maths

Using de Moivre's theorem, show that $$\tan 5 \theta = \frac { 5 \tan \theta - 10 \tan ^ { 3 } \theta + \tan ^ { 5 } \theta } { 1 - 10 \tan ^ { 2 } \theta + 5 \tan ^ { 4 } \theta }$$
Hen esh th the eq tion $x ^ { 2 } - 4 x + 5 = 0$ s ro $\operatorname { stan } ^ { 2 } \left( \frac { 1 } { 5 } \pi \right)$ ad $\operatorname { an } ^ { 2 } \left( \frac { 2 } { 5 } \pi \right)$.