Find all possible triplets such that for all .

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Find all possible triplets (x,y,z)(x,y,z) such that (x+y)+(y+2z)cos⁡2θ+(z−x)sin⁡2θ=0(x+y)+(y+2z)\cos 2\theta+(z-x)\sin^2\theta=0 for all θ\theta.

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