If `cosA=0.6`, find the value of `5sinA-3tan A.`

Answer

To solve the problem where \( \cos A = 0.6 \) and we need to find the value of \( 5 \sin A - 3 \tan A \), we can follow these steps:

### Step 1: Find \( \sin A \)
We know the Pythagorean identity:
\[ \sin^2 A + \cos^2 A = 1 \]
Given \( \cos A = 0.6 \), we can find \( \sin A \):
\[ \sin^2 A = 1 - \cos^2 A \]
Substituting the value of \( \cos A \):
\[ \sin^2 A = 1 - (0.6)^2 = 1 - 0.36 = 0.64 \]
Taking the square root:
\[ \sin A = \sqrt{0.64} = 0.8 \]

### Step 2: Find \( \tan A \)
The tangent function is defined as:
\[ \tan A = \frac{\sin A}{\cos A} \]
Substituting the values we found:
\[ \tan A = \frac{0.8}{0.6} = \frac{8}{6} = \frac{4}{3} \approx 1.33 \]

### Step 3: Substitute values into the expression
Now we substitute \( \sin A \) and \( \tan A \) into the expression \( 5 \sin A - 3 \tan A \):
\[ 5 \sin A - 3 \tan A = 5(0.8) - 3(1.33) \]
Calculating each term:
\[ 5(0.8) = 4 \]
\[ 3(1.33) = 3.99 \]
Now substituting these values:
\[ 5 \sin A - 3 \tan A = 4 - 3.99 = 0.01 \]

### Final Answer
Thus, the value of \( 5 \sin A - 3 \tan A \) is:
\[ \boxed{0.01} \]