# Homework Help: Compound Angles

1. Oct 31, 2012

### odolwa99

In attempting this question, I decided to expand the first statement. Can anyone help me out?

Many thanks.

1. The problem statement, all variables and given/known data

If $\sin A=\sin(A+30^{\circ})$, show that $\tan A=2+\sqrt{3}$.

2. Relevant equations

3. The attempt at a solution

$\sin A=\sin A\cos30+\cos A\sin30$
$\sin A=\frac{\sin A\sqrt{3}+\cos A}{2}$
$2\sin A=\sin A\sqrt{3}+\cos A$
$\sin A(2-\sqrt{3})=\cos A$
$2-\sqrt{3}=\frac{\cos A}{\sin A}$

Last edited: Oct 31, 2012
2. Oct 31, 2012

### CAF123

This implies $$\frac{\sin A}{\cos A} = \frac{1}{2 - \sqrt{3}}.$$ Now rationalise the denominator.

3. Oct 31, 2012

### odolwa99

Great, thank you very much.