To verify the given trigonometric identity involving the tangent function, the first step traditionally would be to express the tangent function of a sum, using the known formula for tangent of the sum of angles.
The relevant tangent addition formula is:
\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \]
Thus, to find \(\tan(x_1 + x_2 + x_3)\), we can first compute \(\tan(x_1 + x_2)\) and then use that result to add \(x_3\):
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First, evaluate \(\tan(x_1 + x_2)\): \[ \tan(x_1 + x_2) = \frac{\tan x_1 + \tan x_2}{1 - \tan x_1 \tan x_2} \]
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Next, use this result to find \(\tan(x_1 + x_2 + x_3)\): \[ \tan(x_1 + x_2 + x_3) = \tan((x_1 + x_2) + x_3) = \frac{\tan(x_1 + x_2) + \tan x_3}{1 - \tan(x_1 + x_2)\tan x_3} \]
Substituting the expression for \(\tan(x_1 + x_2)\) into this equation will help in expanding and ultimately verifying the identity.
Among the options provided, one of the choices will help facilitate this process of verification and simplification.
The correct formation to start verifying the given identity appears to be the one where we can express \(\tan(x_1 + x_2 + x_3)\) as a function of the sum of two angles, i.e.,
\[ \tan(x_1 + x_2 + x_3) = \frac{\tan x_1 + \tan(x_2 + x_3)}{1 - \tan x_1\tan(x_2 + x_3)} \]
Thus, the appropriate first step from the choices given is:
- \(\tan(x_1 + x_2 + x_3) = \frac{\tan x_1 + \tan(x_2 + x_3)}{1 - \tan x_1 \tan(x_2 + x_3)}\)
You should confirm similar expressions based on the relationships of the angles or the corresponding tangent identities.