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A-LevelMathematicsTrigonometry9709/21 · Oct/Nov 2022 · Q34 Marks

It is given that sec θ = √17 where 0 < θ < ½π. Find the exact value of tan(θ + ¼π).

It is given that sec θ = √17 where 0 < θ < ½π. Find the exact value of tan(θ + ¼π).[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[M1] Use identity sec²θ=1+tan²θ to find value of tanθ (OE using cosθ = 1/√17 and sinθ = 4/√17 values.)
[A1] Obtain tanθ = 4 (Condone inclusion of tanθ = -4.)
[M1] State or imply tan(θ+¼π) = (tanθ+tan¼π)/(1-tanθtan¼π) and substitute value of tanθ (OE)
[A1] Obtain -5/3 or exact equivalent only

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About this question

Topic: Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Oct/Nov 2022 Paper 2 Variant 1, question 3.

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