✔ 最佳答案
(a)
其實最主要是看到分子和分母砌埋可以變成 sin (A +/- B)
(sin A cos B)/(cos A sin B) = (4c - b)/b
b sin A cos B + b cos A sin B = 4c cos A sin B
b sin (A + B) = 4c cos A sin B
[sin (A + B)]/c = (4 cos A sin B)/b ......(1)
用正弦公式得 (sin C)/c = sin [180° - (A + B)]/c = [sin (A + B)]/c
再用正弦公式得 (sin C)/c = (sin B)/b
由 (1) 得 (sin B)/b = (4 cos A)(sin B)/b
4 cos A = 1
cos A = 1/4
用餘弦公式得
a² = b² + c² - 2bc cos A
= b² + c² - 2bc(1/4)
= b² + c² - bc/2
(b) 從 (a) 得 cos A = 1/4
A = cos¯¹ (1/4) = 75.5°