✔ 最佳答案
if cosB = sinAsinC,
sin²A - sin²B - cos²C =2sinAcosBsinC - 1
sin²A - (1- cos²B) - (1 - sin²C) = 2sinA(sinAsinC)sinC - 1
sin²A + cos²B + sin²C = 2sin²Asin²C + 1
sin²A + (sinAsinC)² + sin²C = 2sin²Asin²C + 1
sin²A + sin²Asin²C + sin²C = 2sin²Asin²C + 1
sin²A - sin²Asin²C - 1 + sin²C = 0
sin²A(1 - sin²C) - (1-sin²C) = 0
(1-sin²C)(sin²A - 1) = 0
1 - sin²C = 0 or sin²A - 1 = 0
sin²C = 1 or sin²A = 1
sinC = ± 1 or sinA = ± 1
As ABC is a triangle, each angle in triangle ABC < 180°
C = 90°or A = 90°
Therefore, ABC is a right-angled triangle.