Question

Solve the following equations:
cos 2θ = ${\displaystyle \frac{\sqrt{5}+1}{4}}$

Answer 1

We know cos 36° = ${\displaystyle \frac{\sqrt{5}+1}{4}}$, 36° = ${\displaystyle \frac{\pi }{5}}$

cos 2θ = cos 36° = ${\displaystyle \cos \left(\frac{\pi }{5}\right)}$

The general solution is

2θ = ${\displaystyle 2\text{n}\pi \pm \frac{\pi }{5}}$, n ∈ Z

 θ = ${\displaystyle \text{n}\pi \pm \frac{\pi }{10}}$, n ∈ Z