Question

Solve Sec 5theta/4=2

Answer 1

$\sec\dfrac{5\theta}{4}=2\\ \dfrac{1}{\cos \dfrac{5\theta}{4}}=2\\ \cos \dfrac{5\theta}{4}=\dfrac{1}{2}\\ \dfrac{5\theta}{4}=\dfrac{\pi}{3}+2k\pi \vee \dfrac{5\theta}{4}=-\dfrac{\pi}{3}+2k\pi\\ 5\theta=\dfrac{4\pi}{3}+8k\pi \vee 5\theta=-\dfrac{4\pi}{3}+8k\pi\\ \boxed{\theta=\dfrac{4\pi}{15}+\dfrac{8k\pi}{5} \vee \theta=-\dfrac{4\pi}{15}+\dfrac{8k\pi}{5}}$