Find all solutions of the equation in the interval [0, 2π) (express your answer in terms of $k$, where $k$ is any integer).
$$\cos 2\theta + 7 \cos\theta = 8$$
Did I make a mistake somewhere? My final answer was $0+2\pi k$
Here is my work. I went from step 1 to step 2 by using the trig identity $\cos 2\theta = 2\cos^2\theta -1$ and then solved it like a quadratic. I also set $\cos \theta = x$ because it's easier for me to visualize the equation that way.
Best Answer
Your final answer is correct $\boxed{\theta=2 \pi n} , \; n \in \mathbb{Z}$
you also have:
$\theta=\bigg(\pi n \pm i \arctan \text{h}\sqrt{\frac{11}{7}}\bigg)$
In your homework the interval is $[0,2 \pi)$ so you only have $\boxed0$ as solution