Problem
Solution
For this case we can do the following:
[tex]\frac{1}{\cos\theta}\cdot\frac{\sin\theta}{\cos\theta}-\cos \theta\cdot\frac{\cos\theta}{\sin\theta}=\sin \theta[/tex][tex]\frac{\sin\theta}{cos^2\theta}-\frac{\cos^2\theta}{\sin\theta}=\sin \theta[/tex][tex]\frac{\sin^2\theta-\cos^2\theta\cos^2\theta}{\sin\theta\cos^2\theta}=\sin \theta[/tex]
then we can croos multiply:
[tex]\sin ^2\theta-\cos ^2\theta\cos ^2\theta=\sin ^2\theta\cos ^2\theta[/tex]
then we can redistribute the terms and we got:
[tex]\sin ^2\theta=\cos ^2\theta\cos ^2\theta+\sin ^2\theta\cos ^2\theta[/tex]
taking common factor cos^2 we got:
[tex]\sin ^2\theta=\cos ^2\theta(\cos ^2\theta+\sin ^2\theta)[/tex]
Since:
[tex]\sin ^2\theta+\cos ^2\theta=1[/tex]
We have:
[tex]\sin ^2\theta=\cos ^2\theta[/tex]
And thae answer for this case is:
[tex]\theta=\frac{\pi}{4}+\pi\text{ n}[/tex]
