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Official 2021 Paper 2 · Q19

Paper 2Logic & proofTrigonometryGeometry

The angle θ\theta can take any of the values 1∘,2∘,3∘,…,359∘,360∘1^\circ,2^\circ,3^\circ,\ldots,359^\circ,360^\circ.

For how many of these values of θ\theta is it true that

sin⁡θ1+sin⁡θ1−sin⁡θ+cos⁡θ1+cos⁡θ1−cos⁡θ=0?\sin\theta\sqrt{1+\sin\theta}\sqrt{1-\sin\theta}+\cos\theta\sqrt{1+\cos\theta}\sqrt{1-\cos\theta}=0?
A00
B11
C22
D44
E9393
F182182
G271271
H360360

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