If , then is equal…

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

Problem

If sin⁡αsin⁡β=cos⁡γcos⁡δ\frac{\sin \alpha}{\sin \beta} = \frac{\cos \gamma}{\cos \delta} , then sin⁡(α−β2)⋅cos⁡(α+β2)⋅cos⁡δsin⁡(δ−γ2)⋅sin⁡(δ+γ2)⋅sin⁡β\frac{\sin \left( \frac{\alpha - \beta}{2} \right) \cdot \cos \left( \frac{\alpha + \beta}{2} \right) \cdot \cos \delta}{\sin \left( \frac{\delta - \gamma}{2} \right) \cdot \sin \left( \frac{\delta + \gamma}{2} \right) \cdot \sin \beta} is equal to

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