What is the value of $$\frac{\left\{(\sin 4x + \sin 4y) [(\tan 2x - 2y)]\right\}}{(\sin 4x - \sin 4y)}$$?
$$\frac{\left\{(\sin4x+\sin4y)[(\tan2x-2y)]\right\}}{(\sin4x-\sin4y)}$$
$$=\frac{2\times\sin\left(\frac{4x+4y}{2}\right)\times\ \cos\left(\frac{4x-4y}{2}\right)\left(\tan2x-2y\right)}{2\times\ \cos\left(\frac{4x+4y}{2}\right)\times\sin\left(\frac{4x-4y}{2}\right)}\ .$$
$$=\tan\left(2x+2y\right).\cot\left(2x-2y\right).\tan\left(2x-2y\right)\ .$$
$$=\tan\left(2x+2y\right)\ .$$
D is correct choice.
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