Which of the following is the correct identity for ?

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

Problem

Which of the following is the correct identity for cos⁡α−cos⁡β  \cos\alpha-\cos\beta\;? (a) 2cos⁡α+β2 cos⁡α−β22\cos\dfrac{\alpha+\beta}{2}\,\cos\dfrac{\alpha-\beta}{2} (b) 2sin⁡α+β2 sin⁡α−β22\sin\dfrac{\alpha+\beta}{2}\,\sin\dfrac{\alpha-\beta}{2} (c) −2sin⁡α+β2 sin⁡α−β2-2\sin\dfrac{\alpha+\beta}{2}\,\sin\dfrac{\alpha-\beta}{2} (d) −2sin⁡α+β2 cos⁡α−β2-2\sin\dfrac{\alpha+\beta}{2}\,\cos\dfrac{\alpha-\beta}{2}

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