2021 · Q59
If A, B and C are interior angles of a triangle ABC, then what is tan((B + C)/2) + sin((B + C)/2) − cot(A/2) − cos(A/2) equal to ?
Elementary MathematicsTrigonometry
- A0
- B1/2
- Csin((A + B + C)/4)
- Dtan((A + B + C)/4)
Explanation
Since A + B + C = 180°, (B+C)/2 = 90° − A/2. Then tan((B+C)/2) = cot(A/2) and sin((B+C)/2) = cos(A/2). The expression is [cot(A/2) − cot(A/2)] + [cos(A/2) − cos(A/2)] = 0. This is option (a).