Question

Not sure how to solve 2sinxcosx+cosx=0  Could you help?

Answer 1

`2sinxcosx+cosx=0\\\\cosx(2sinx+1)=0\iff cosx=0\ \vee\ 2sinx+1=0\\\\cosx=0\ \vee\ 2sinx=-1\ /:2\\\\cosx=0\ \vee\ sinx=-(1)/(2)\\\\x=(\pi)/(2)+k\pi\ \vee\ x=-(\pi)/(6)+2k\pi\ \vee\ x=(7\pi)/(6)+2k\pi\ to\ k\in\mathbb{Z}`