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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

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    Hint: you should eventually arrive at the equation $\tan\theta=\sqrt{3}$.2012-11-12
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    Wimbledon vs. York are going into extra time. FA cup.2012-11-12
  • 0
    Your problem lies with the substitution of $\cos\theta$ by $1-\sin\theta$. You're confusing it with $\cos^2\theta \equiv 1-\sin^2\theta$.2012-11-12

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