Question

what is the solution of the following trig equation: tan(theta)(csc(theta)+2)=0

Answer 1

`D:\theta\\eq(k\pi)/(2);\ k\in\mathbb{Z}\\\\tan\theta(csc\theta+2)=0\iff tan\theta=0\ \vee\ csc\theta+2=0\\\\\\tan\theta=0\iff\theta=k\pi\\otin D\\\\csc\theta+2=0\\\\csc\theta=-2\\\\(1)/(sin\theta)=-2\\\\-2sin\theta=1\ /:(-2)\\\\sin\theta=-(1)/(2)`


`(\theta=-(\pi)/(6)+2k\pi\ \vee\ \theta=(7\pi)/(6)+2k\pi)-answer`