Question

Sin(θ) cos(3θ) + cos(θ) sin(3θ) = 0

Answer 1

`\displaystyle\\ \text{We use formula:}\\ \sin(\alpha+\beta)=\sin(\alpha)\cos(\beta)+cos(\alpha)\sin(\beta)\\\\ Resolve:\\\\ \sin(\Theta)cos(3\Theta)+cos(\Theta)sin(3\Theta)=0\\\\ \sin(\Theta+3\Theta)=0\\\\ \sin(4\Theta)=0\\\\ \text{We have two solutions:}\\\\ 4\Theta=0~~\Longrightarrow~~\Theta=(0)/(4)=0~~\Longrightarrow~~ \boxed{\Theta_1=0+2k\pi}\\\\ 4\Theta=\pi~~\Longrightarrow~~\Theta=(\pi)/(4)~~\Longrightarrow~~ \boxed{\Theta_2=(\pi)/(4)+2k\pi}\\\\`