Hello please help me with these trig identities and double angles as I am not sure where I am going wrong but I keep getting the wrong answer
This is the problem $$ \sin(\theta+30) = 2\cos(\theta) $$ This is my one of my incorrect solutions
$$\sin(\theta +30) = 2\cos(\theta)$$ $$\sin(\theta)\cos(30) + \sin(30)\cos(\theta)=2(1 - \sin(\theta))$$ $$\sin(\theta)(\frac{\sqrt3}{2})+(\frac{1}{2})(1 - \sin(\theta))=2-2\sin(\theta)$$ $$\frac{\sin(\theta)\sqrt3+1-\sin(\theta)}{2}+2 \sin(\theta)=2$$
I get stuck and I am not sure what to do with this problem.
Please help as I am trying to self teach my A -level maths.
Thanks in advance