If `sinA=b,` what is the value of product `sinA*cosA*tanA` in terms of b?

Options

A. `1`
B. `(1)/(b)`
C. `b`
D. `b^(2)`

Answer

To find the value of the product \( \sin A \cdot \cos A \cdot \tan A \) in terms of \( b \), where \( \sin A = b \), we can follow these steps:

### Step 1: Write down the expression
We start with the expression we need to evaluate:
\[ \sin A \cdot \cos A \cdot \tan A \]

### Step 2: Substitute the definition of \( \tan A \)
Recall that \( \tan A = \frac{\sin A}{\cos A} \). We can substitute this into our expression:
\[ \sin A \cdot \cos A \cdot \tan A = \sin A \cdot \cos A \cdot \left(\frac{\sin A}{\cos A}\right) \]

### Step 3: Simplify the expression
Now, we can simplify the expression:
\[ \sin A \cdot \cos A \cdot \left(\frac{\sin A}{\cos A}\right) = \sin A \cdot \frac{\sin A \cdot \cos A}{\cos A} \]
The \( \cos A \) in the numerator and denominator cancels out:
\[ = \sin^2 A \]

### Step 4: Substitute \( \sin A \) with \( b \)
Since we are given that \( \sin A = b \), we can substitute \( b \) into the expression:
\[ \sin^2 A = b^2 \]

### Conclusion
Thus, the value of the product \( \sin A \cdot \cos A \cdot \tan A \) in terms of \( b \) is:
\[ b^2 \]