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Official 2022 Paper 1 · Q9

Paper 1Trigonometry

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

f(x)−g(x)=2sin⁡xf(x)g(x)=cos⁡2x\begin{aligned}f(x)-g(x)&=2\sin x\\f(x)g(x)&=\cos^2x\end{aligned}

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?

A1−21-\sqrt2
B−1−2-1-\sqrt2
C00
D−1-1
E−2-2
F−3-3
G−4-4

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