Problem

$\frac{\tan 2 x-\tan x}{1+\tan 2 x \tan x}=$

Answer

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Answer

\(\boxed{\tan(-x)}\) is the final answer.

Steps

Step 1 ：Given the expression \(\frac{\tan 2 x-\tan x}{1+\tan 2 x \tan x}\)

Step 2 ：This is a trigonometric identity problem. The expression given is a standard trigonometric identity for \(\tan(x-y)\).

Step 3 ：So, we can simplify the expression to \(\tan(x - 2x)\).

Step 4 ：However, we know from trigonometric identities that \(\frac{\tan a - \tan b}{1 + \tan a \tan b} = \tan(a - b)\).

Step 5 ：So, we can manually simplify the expression to \(\tan(x - 2x) = \tan(-x)\).

Step 6 ：\(\boxed{\tan(-x)}\) is the final answer.

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