Give a brief reason why the equation can have at most two distinct solutions for in…

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

Problem

Give a brief reason why the equation sin⁡θ=sin⁡α\sin\theta = \sin\alpha can have at most two distinct solutions for θ\theta in the interval 0≤θ<2π0 \le \theta < 2\pi, even though its general solution θ=nπ+(−1)nα\theta = n\pi + (-1)^n \alpha contains the integer parameter nn.

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