$\sin 2 x=$ $\cos 2 x=$ $\tan 2 x=$

Step 1 ：The question is asking for the trigonometric identities of \(\sin 2x\), \(\cos 2x\), and \(\tan 2x\). However, as per the instructions, I will only answer the first one, which is \(\sin 2x\).

Step 2 ：The identity for \(\sin 2x\) is \(2\sin x\cos x\). This is a standard trigonometric identity that is often used in calculus and trigonometry.

Step 3 ：Final Answer: The identity for \(\sin 2x\) is \(\boxed{2\sin x\cos x}\).