Question

Problem Solving

Answer 1

Answer:

A) $\theta=30^\circ+180n^\circ$

Step-by-step explanation:

$tan\theta=4tan\theta-\sqrt{3}\\\\-3tan\theta=-\sqrt{3}\\\\9tan^2\theta=3\\\\tan^2\theta=\frac{3}{9}\\ \\tan^2\theta=\frac{1}{3}\\ \\\frac{1-cos(2\theta)}{1+cos(2\theta)}=\frac{1}{3}\\ \\ 3-3cos(2\theta)=1+cos(2\theta)\\\\2-3cos(2\theta)=cos(2\theta)\\\\2=4cos(2\theta)\\\\\frac{2}{4}=cos(2\theta)\\ \\\frac{1}{2}=cos(2\theta)\\ \\2\theta=60^\circ+360n^\circ\\\\\theta=30^\circ+180n^\circ$

Recall the identity $tan^2(\theta)=\frac{1-cos(2\theta)}{1+cos(2\theta)}$