Question

Solve Sec 5theta/4=2

Answer 1

`\sec(5\theta)/(4)=2\\ (1)/(\cos (5\theta)/(4))=2\\ \cos (5\theta)/(4)=(1)/(2)\\ (5\theta)/(4)=(\pi)/(3)+2k\pi \vee (5\theta)/(4)=-(\pi)/(3)+2k\pi\\ 5\theta=(4\pi)/(3)+8k\pi \vee 5\theta=-(4\pi)/(3)+8k\pi\\ \boxed{\theta=(4\pi)/(15)+(8k\pi)/(5) \vee \theta=-(4\pi)/(15)+(8k\pi)/(5)}`