Question

Please help!! 15 points!!

Answer 1

Here's the solution in attachment :

Answer 2

$- 1 = - 3 - 4 \cos(4θ + \frac{2\pi}{3} ) \\ - 1 + 4 \cos(4θ + \frac{2\pi}{3} ) = - 3 \\ 4 \cos(4θ + \frac{2\pi}{3} ) = - 3 + 1 \\ 4 \cos(4θ + \frac{2\pi}{3} ) = - 2 \\ \cos(4θ + \frac{2\pi}{3} ) = - \frac{1}{2} \\ \cos(4θ + \frac{2\pi}{3} ) = - \frac{1}{2} \\ \cos(2\pi - (4θ + \frac{2\pi}{3} )) = - \frac{1}{2} \\ 4θ + \frac{2\pi}{3} = arccos( - \frac{1}{2} ) \\ \cos( \frac{4\pi}{3} - 4θ) = - \frac{1}{2}$