Answer:
Step-by-step explanation:
[tex]\frac{cos^2 \theta}{(cot^2 \theta-cos^2 \theta)} \\=\frac{cos^2 \theta}{\frac{cos^2 \theta}{sin^2 \theta } -cos^2 \theta} \\=\frac{cos ^2\theta *sin^2 \theta}{cos^2 \theta (1-sin^2 \theta)} \\=\frac{sin ^2 \theta}{1-sin ^2 \theta} \\=\frac{sin^2 \theta}{cos^2 \theta} \\=tan ^2 \theta[/tex]
[tex]tan^2 \theta=3\\tan \theta=\pm \sqrt{3} \\tan \theta=\sqrt{3} =tan \frac{\pi }{3} ,tan (\pi +\frac{\pi }{3} )\\\theta=\pi /3,4\pi /3\\tan \theta=-\sqrt{3} =tan (\pi-\frac{\pi}{3} ),tan (2\pi -\frac{\pi}{3} )\\\theta=2 \pi/3,5\pi/3[/tex]
