<s>[INST] If $p =\frac{4\sin\theta \cos\theta}{\sin\theta +\cos\theta}$ Find the value of $\frac{p+2\sin\theta}{p-2\sin\theta}$ Problem : 

If $\displaystyle p =\frac{4\sin\theta\cos\theta}{\sin\theta +\cos\theta}$, find the value of $\displaystyle \frac{p+2\sin\theta}{p-2\sin\theta} + \frac{p+2\cos\theta}{p-2\cos\theta}$.

Please help how to proceed in such problem..Thanks..
 [/INST] Note that $$\frac{p}{2\cos\theta}=\frac{2\sin \theta}{\cos\theta+\sin\theta}$$ and 
$$\frac{p}{2\sin\theta}=\frac{2\cos \theta}{\cos\theta+\sin\theta}$$
Now apply the componendo-dividendo method to the first and second equalities and sum them up, you'll get the answer. It'll be $2$.
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