Some A level students were given the following question - Edexcel - A-Level Maths Pure - Question 4 - 2017 - Paper 2
Question 4
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... show full transcript
Worked Solution & Example Answer:Some A level students were given the following question - Edexcel - A-Level Maths Pure - Question 4 - 2017 - Paper 2
Step 1
Identify an error made by student A.
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Answer
Student A incorrectly attempts to solve the equation by using the ratio sinθcosθ=tanθ. The correct approach should express cosθ in terms of sinθ or vice versa, rather than setting up this incorrect ratio.
Step 2
Explain why this answer is incorrect.
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Answer
The value −26.6∘ cannot be a solution because it falls outside the allowable range of −90∘<θ<90∘. Furthermore, even though sinθ can yield positive or negative values, the equation cosθ=2sinθ restricts valid solutions further.
Step 3
Explain how this incorrect answer arose.
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Answer
The incorrect answer arose from the squaring of both sides of the equation, which can introduce extraneous solutions. Squaring cosθ=2sinθ led to the equation cos2θ=4sin2θ, which is valid, but the process may introduce solutions that do not satisfy the original equation. As seen, squaring both sides yields an additional solution that did not hold true in the original equation.
