2. Some A level students were given the following question.
Solve, for \(- 90 ^ { \circ } < \theta < 90 ^ { \circ }\), the equation
$$\cos \theta = 2 \sin \theta$$
The attempts of two of the students are shown below.
| \(\underline { \text { Student } A }\) |
| \(\cos \theta = 2 \sin \theta\) |
| \(\tan \theta = 2\) |
| \(\theta = 63.4 ^ { \circ }\) |
Student \(B\)
$$\begin{aligned}
\cos \theta & = 2 \sin \theta
\cos ^ { 2 } \theta & = 4 \sin ^ { 2 } \theta
1 - \sin ^ { 2 } \theta & = 4 \sin ^ { 2 } \theta
\sin ^ { 2 } \theta & = \frac { 1 } { 5 }
\sin \theta & = \pm \frac { 1 } { \sqrt { 5 } }
\theta & = \pm 26.6 ^ { \circ }
\end{aligned}$$
- Identify an error made by student \(A\).
Student \(B\) gives \(\theta = - 26.6 ^ { \circ }\) as one of the answers to \(\cos \theta = 2 \sin \theta\).
- Explain why this answer is incorrect.
- Explain how this incorrect answer arose.