Question

In a \( \triangle ABC \), if \( 2 \cos C = \sin B \cdot \csc A \), then

• A. \( a = b \)
• B. \( b = c \)
• C. \( a = c \)
• D. \( a = b = c \)

Hint:

When dealing with trigonometric relations in triangles, use the sine and cosine rules to simplify the expressions and determine relationships between the sides and angles.

Answer 1

The Correct Option is C

Step 1: Analyze the given condition.
The given condition is \( 2 \cos C = \sin B \cdot \csc A \). By using the sine rule in the triangle and simplifying the equation, we can find that \( a = c \). This shows that sides \( a \) and \( c \) are equal.

Step 2: Conclusion.
Thus, the correct answer is \( a = c \), corresponding to option (C).