Question

In a triangle ABC, \( 5 \cos C + 6 \cos B = 4 \) and \( 6 \cos A + 4 \cos C = 5 \), then:

• A. \( \frac{3}{2} \)
• B. \( 1 \)
• C. \( \frac{3}{4} \)
• D. \( 5 \)

Hint:

For solving trigonometric equations involving angles of a triangle, use known identities and properties of triangle angles.

Answer 1

The Correct Option is C

Step 1: Use trigonometric identities. Use the given equations to solve for the angles of the triangle and find the value of \( \tan \frac{A}{2} \).
Step 2: Conclusion. Thus, the value of \( \tan \frac{A}{2} \) is \( \frac{3}{4} \).