Which of the following expressions is equal to ?

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Which of the following expressions is equal to 2cos⁡αsin⁡β2\cos\alpha\sin\beta? (a) sin⁡(α+β)+sin⁡(α−β)\sin(\alpha+\beta)+\sin(\alpha-\beta) (b) sin⁡(α+β)−sin⁡(α−β)2\displaystyle\frac{\sin(\alpha+\beta)-\sin(\alpha-\beta)}{2} (c) sin⁡(α+β)−sin⁡(α−β)\sin(\alpha+\beta)-\sin(\alpha-\beta) (d) cos⁡(α+β)+cos⁡(α−β)\cos(\alpha+\beta)+\cos(\alpha-\beta)

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