CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 2 · Question 3(a)
Given that tan² x = sin² x / (1 - sin² x), show that sin x = ± tan x / √(1 + tan² x).
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- 3(b)(i)Show that f(θ) = √3 sin θ + cos θ may be expressed as f(θ) = 2sin(θ + π/6) where 0 ≤ θ ≤ π/2.[6 marks]
- 3(b)(ii)a)solve the equation f(θ) = √2 for 0 ≤ θ ≤ 2π[5 marks]
- 3(b)(ii)b)determine the maximum value of f and the smallest positive value of θ for which it occurs.[3 marks]
- 3(c)Without the use of a calculator or tables, find the exact value of cos(π/12).[5 marks]
More practice: the rest of this paper · more Trigonometric Functions, Identities and Equations questions · all CAPE Pure Mathematics Unit 1 past papers