$7 \tan x \cos x=5$
\(\boxed{x \approx 0.7956}\)
Step 1 :Rewrite the equation in terms of sine and cosine: \(7 \frac{\sin x}{\cos x} \cos x = 5\)
Step 2 :Simplify the equation: \(7 \sin x = 5\)
Step 3 :Divide both sides by 7: \(\sin x = \frac{5}{7}\)
Step 4 :Find the value of x: \(x \approx 0.7956\)
Step 5 :\(\boxed{x \approx 0.7956}\)