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Beyond Horizon Set 2 Paper 1 · Q8

Paper 1Trigonometry

This question is about pairs of functions ff and gg that satisfy

f(x)−g(x)=3sin⁡xf(x)-g(x)=3\sin x
f(x)g(x)=cos⁡2xf(x)g(x)=\cos^2x

for all real numbers xx. Across all solutions for f(x)f(x), what is the minimum value that f(x)f(x) attains for any xx?

A1−31-\sqrt3
B−1−3-1-\sqrt3
C00
D−1-1
E−2-2
F−3-3
G−4-4

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