If `A + B=90^(@) and cos B=1//3`, then the value of `sin A` is
A. 1/2
B. 1/4
C. 1/3
D. 2/3

Options

A. C
B. B
C. D
D. A

Answer

To solve the problem, we start with the given information:

1. **Given**: \( A + B = 90^\circ \)
2. **Given**: \( \cos B = \frac{1}{3} \)

We need to find the value of \( \sin A \).

### Step 1: Use the Complementary Angle Identity
Since \( A + B = 90^\circ \), we can use the complementary angle identity for cosine and sine:
\[ \cos B = \sin A \]

### Step 2: Substitute the Value of \( \cos B \)
From the problem, we know that:
\[ \cos B = \frac{1}{3} \]
Thus, we can substitute this value into the identity:
\[ \sin A = \cos B = \frac{1}{3} \]

### Conclusion
The value of \( \sin A \) is:
\[ \sin A = \frac{1}{3} \]

### Answer
The correct option is C. \( \frac{1}{3} \).

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