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tmua.me Medium Set A Paper 2 · Q15

Paper 2Trigonometry

What is the sum of cos⁡2θ\cos^2\theta over all the distinct solutions of

cos⁡2θ=∣sin⁡θ−12∣\cos^2\theta=\left|\sin\theta-\frac12\right|

for which 0≤θ<2π0\leq\theta<2\pi?

A7+3−22\dfrac{\sqrt7+\sqrt3-2}{2}
B6−7−36-\sqrt7-\sqrt3
C3\sqrt3
D7+3−2\sqrt7+\sqrt3-2
E7−2\sqrt7-2
F2+7−32+\sqrt7-\sqrt3

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