CAPE Pure Mathematics Unit 1 · May/June 2016 · Paper 2 · Question 3(b)(i)
Express the function f(θ) = sinθ + cosθ in the form r sin(θ + α), where r > 0 and 0 ≤ α ≤ π/2.
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- 3(a)(i)Show that sec²θ = cosecθ / (cosecθ - sinθ).[4 marks]
- 3(a)(ii)Hence, or otherwise, solve the equation cosecθ / (cosecθ - sinθ) = 4/3 for 0 ≤ θ ≤ 2π.[5 marks]
- 3(b)(ii)Hence, find the maximum value of f and the smallest non-negative value of θ at which it occurs.[5 marks]
- 3(c)Prove that tan(A + B + C) = (tanA + tanB + tanC - tanA tanB tanC) / (1 - tanA tanB - tanA tanC - tanB tanC).[6 marks]
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