Identify error in student working

A question is this type if and only if it presents a student's (incorrect or incomplete) solution to a quadratic trig equation and asks the candidate to identify and explain the errors made.

1 questions · Easy -1.2

1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals
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Edexcel Paper 2 Specimen Q2
3 marks Easy -1.2
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 \(B\) $$\begin{aligned} \cos \theta & = 2 \sin \theta \\ \cos ^ { 2 } \theta & = 4 \sin ^ { 2 } \theta \\ 1 - \sin ^ { 2 } \theta & = 4 \sin ^ { 2 } \theta \\ \sin ^ { 2 } \theta & = \frac { 1 } { 5 } \\ \sin \theta & = \pm \frac { 1 } { \sqrt { 5 } } \\ \theta & = \pm 26.6 ^ { \circ } \end{aligned}$$
  1. Identify an error made by student \(A\). Student \(B\) gives \(\theta = - 26.6 ^ { \circ }\) as one of the answers to \(\cos \theta = 2 \sin \theta\).
    1. Explain why this answer is incorrect.
    2. Explain how this incorrect answer arose.