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$Sin α = \sin β, \cos α = \cos β then$

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$\cos (\frac{(α + β)}{2}) = 0$

$\cos (\frac{(α - β)}{2}) = 0$

$\sin (\frac{(α - β)}{2}) = 0$

$\sin \frac{(α + β)}{2} = 0$

answer is C.

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Detailed Solution

$Sin α - \sin β = 0 \Rightarrow 2 \cos \frac{α + β}{2} \sin \frac{α - β}{2} = 0 \cos α - \cos β =0⇒- 2 \sin \frac{α + β}{2} \sin \frac{α - β}{2} = 0 From the above 2 equations \sin (\frac{(α - β)}{2}) = 0$

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