trigonometry

Question: If $\sin \theta +\sin \varphi =a$and $\cos \theta +\cos \varphi =b,$then $\tan \frac{\theta -\varphi }{2}$is equal to

1) $\sqrt{\frac{{{a}^{2}}+{{b}^{2}}}{4-{{a}^{2}}-{{b}^{2}}}}$

2) $\sqrt{\frac{4-{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}$

3) $\sqrt{\frac{{{a}^{2}}+{{b}^{2}}}{4+{{a}^{2}}+{{b}^{2}}}}$

4) $\sqrt{\frac{4+{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}$

Solution:

Explanation: No Solution

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