A-LevelMathematicsTrigonometry9709/33 · May/June 2019 · Q37 Marks
Let f(θ) = (1 - cos 2θ + sin 2θ) / (1 + cos 2θ + sin 2θ)
- (i)Show that f(θ) = tan θ.[3]
- (ii)Hence show that ∫_(π/6)^(π/4) f(θ) dθ = (1/2) ln (√3 / 2).[4]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [M1] Use double angle formulae and express entire fraction in terms of sin θ and cos θ
- [A1] Obtain a correct expression
- [A1] Obtain the given answer
- [M1*] State integral of the form ±ln cos θ
- [DM1] Use correct limits correctly and insert exact values for the trig ratios
- [A1] Obtain a correct expression, e.g. -ln (1/√2) + ln (√3/2)
- [A1] Obtain the given answer following full and exact working
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