I have to prove the following trigonometric identities. However, since I can't prove them, I am starting to think they are not correctly stated.
Problem 1:
$$\cos\frac{2π}{3}+\cos\frac{4π}{9}+\cos\frac{6π}{3}+\cos\frac{8π}{9}=-\frac{1}{2}$$
Problem 2:
$$\frac{\cot^2\frac{α}{2}-\cot\frac{3α}{2}}{\cos^2\frac{α}{2}\cosα(1+\cot^2\frac{3α}{2})}=8$$
The first formula is correct, if we assume it is a typo.
Problem 1:
$$\cos\frac{2π}{3}+\cos\frac{4π}{3}+\cos\frac{6π}{3}+\cos\frac{8π}{3}=-\frac{1}{2}$$
Sum of $n$ angles in $ AP == \dfrac{\sin n \beta/2}{\sin \beta/2} \cos ( Average Angle)$. Here angle is in degrees.
$$ \dfrac{\sin(4\cdot 120/2)}{\sin (120/2)}\cos{300} = -\frac{1}2 $$
