A-LevelMathematicsTrigonometry9709/32 · May/June 2021 · Q67 Marks
Prove that cosec 2θ − cot 2θ = tan θ.
- (a)Prove that cosec 2θ − cot 2θ = tan θ.[3]
- (b)Hence show that ∫^(π/3)_(π/6) (cosec 2θ − cot 2θ) dθ = ½ ln 2.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [B1] Express the LHS in terms of cos 2θ and sin 2θ
- [M1] Use correct double angle formulae to express the LHS in terms of cos θ and sin θ
- [A1] Obtain tan θ from correct working
- [M1] State integral of the form ±ln cos θ or ±ln sec θ
- [DM1] Use correct limits correctly and insert exact values for the trigonometric ratios
- [A1] Obtain a correct expression, e.g. −ln(½) + ln(1/√2)
- [A1] Obtain ½ ln 2 from correct working
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