Question

Can someone please give me the answer to the second part of this question? Thank You!

Answer 1

Answer:

$\theta=30\textdegree$

Step-by-step explanation:

$(ii)\ \sqrt{3}\tan\ \theta=2\sin \theta\\\\substitute\ \tan\theta=\frac{\sin\theta}{\cos\theta}\\\\\sqrt{3}\frac{\sin\theta}{\cos\theta}=2\sin\theta\\\\Divide\ both\ sides\ by\ \sin\theta.\\\\\sqrt{3}\frac{\sin\theta}{\cos\theta\times \sin\theta}=\frac{2\sin\theta}{\sin\theta}\\\\\frac{\sqrt{3}}{\cos\theta}=\frac{2}{1}\\\\Apply\ cross\ multiplication\\\\2\cos\theta=\sqrt{3}\\\\divide\ both\ sides\ by\ 2\\\\\frac{2\cos\theta}{2}=\frac{\sqrt{3}}{2}\\\\\cos\theta=\frac{\sqrt{3}}{2}$

$\cos\theta=\cos\ 30\textdegree\\\\\theta=30\textdegree$