A-LevelMathematicsTrigonometry9709/23 · May/June 2020 · Q810 Marks
Show that 3 sin 2θ cot θ = 6 cos² θ.
- (a)Show that 3 sin 2θ cot θ = 6 cos² θ.[2]
- (b)Solve the equation 3 sin 2θ cot θ = 5 for 0 < θ < π.[3]
- (c)Find the exact value of ∫(from π/4 to π/2) 3 sin x cot ½x dx.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- Use at least one of sin 2θ = 2 sin θ cos θ and cot θ = cos θ / sin θ
- Use both and conclude 6 cos² θ AG
- Attempt solution of cos² θ = 5/6 to find at least one value
- Obtain 0.421
- Obtain 2.72
- Express integrand in form a + b cos x
- Obtain correct integrand 3 + 3 cos x
- Integrate to obtain px + q sin x
- Apply limits correctly
- Obtain ¾π + 3 - 3/√2 or exact equivalent
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