1. If \(r \cos θ = 2\sqrt{3}\), \(r \sin θ = 2\), and \(0^\circ < θ < 90^\circ\), then find the values of \(r\) and \(θ\).

2. If \(r\cosθ = 1\) and \(r\sinθ = \sqrt{3}\), then find the values of \(r\) and \(θ\).

3. If \( r\cosθ = 2\sqrt{3} \), \( r\sinθ = 2 \), and \( 0^\circ < θ < 90^\circ \), then find the values of \( r \) and \( θ \).

4. If \( r \cos θ = 2\sqrt{3} \), \( r \sin θ = 2 \), and \( 0° < θ < 90° \), then find the values of both \( r \) and \( θ \).

5. If \(r \cos \theta = \frac{1}{2}\) and \(r \sin \theta = \frac{\sqrt{3}}{2}\), then find the value of \(r\), where \(0^\circ < \theta < 90^\circ\).

6. If \( r \cos\theta = 2\sqrt{3} \), \( r \sin\theta = 2 \), and \( 0^\circ < \theta < 90^\circ \), then find the values of \( r \) and \( \theta \).

7. If \( \csc^2 θ = 2\cot θ \) and \( 0° < θ < 90° \), then find the value of \( θ \).

8. If \(\cot θ = 2\), then find the values of \(\tan θ\) and \(\sec θ\), and show that: \[1 + \tan^2θ = \sec^2θ\]