Question

Solve the following:
2cosx+sin(2x)=0

Step by Step explanation please

Answer 1

\[2\cos(x)+\sin(2x)=0\]you want to work it out together?

Answer 2

At first, there is a rule,\[\sin(a+b)=\sin(a)\cos(b)+\sin(b)\cos(a)\]in your case, however, the "a" and "b" are both "x", so you get,
\[\sin(2x)=\sin(x+x)=\sin(x)\cos(x)+\sin(x)\cos(x)=2\sin(x)\cos(x)\]So you can re-write your question as,\[2\cos(x)+2\sin(x)\cos(x)=0\]factor out of 2cos(x), and you get,\[2\cos x(\sin x)=0\]
So either,\[2\cos(x)=0~~~~~~~~~or~~~~~~~~~~\sin(x)=0\]

Answer 3

you should be able to do it from here for the least part.