Para un ángulo $x$ determine $\operatorname{sen}(2 x), \cos (2 x) y \tan (2 x)$. sabiendo que $\tan x=-\frac{7}{8}$ y $\cos x>0$.

Step 1 ：We are given that \(\tan(x) = -\frac{7}{8}\) and \(\cos(x) > 0\).

Step 2 ：From the given, we can find the values of \(\sin(x)\) and \(\cos(x)\) using the Pythagorean identity \(\sin^2(x) + \cos^2(x) = 1\).

Step 3 ：Since \(\cos(x) > 0\) and \(\tan(x) < 0\), we know that \(\sin(x) < 0\) (because in the unit circle, cosine is positive in the first and fourth quadrants, and tangent is negative in the fourth quadrant, so x must be in the fourth quadrant where sine is negative).

Step 4 ：After finding \(\sin(x)\) and \(\cos(x)\), we can use the double angle formulas to find \(\sin(2x)\), \(\cos(2x)\) and \(\tan(2x)\):

Step 5 ：\(\sin(2x) = 2\sin(x)\cos(x)\)

Step 6 ：\(\cos(2x) = \cos^2(x) - \sin^2(x)\)

Step 7 ：\(\tan(2x) = \frac{\sin(2x)}{\cos(2x)}\)

Step 8 ：Let's calculate these step by step.

Step 9 ：\(\tan(x) = -0.875\)

Step 10 ：\(\cos(x) = 0.7525766947068778\)

Step 11 ：\(\sin(x) = 0.658504607868518\)

Step 12 ：\(\sin(2x) = 0.991150442477876\)

Step 13 ：\(\cos(2x) = 0.13274336283185845\)

Step 14 ：\(\tan(2x) = 7.466666666666663\)

Step 15 ：Final Answer: The values of \(\sin(2x)\), \(\cos(2x)\) and \(\tan(2x)\) are approximately \(\boxed{0.991}\), \(\boxed{0.133}\) and \(\boxed{7.467}\) respectively.