若sinA+cosA=tanA(0
问题描述：
若sinA+cosA=tanA(0
答
sin a + cos a = tan a
sin a + cos a = sin a / cos a
sin a .cos a + cos a .cos a = sin a
sin a .cos a + 1 - sin a .sin a = sin a
cos a = (sin a .sin a + sin a - 1)/sin a
cos a = sin a + 1 - 1/sin a
0° 0 若 a = 90°,sin a = 1,
那么 cos a = 1 + 1 - 1 = 1
矛盾!
sin a + 1 = 1/sin a
sin a .sin a + sin a = 1
sin a .sin a + sin a - 1 = 0
sin a = ( -1 + √5)/2
a = 38.17°或 141.83°
若 0°sin a + 1 cos a ∵ 当 90°∴ 141.83°若 38.17°sin a + 1 > 1/sin a,
cos a > 0
∵ 当 0°∴ 38.17°=> a 的范围：38.17°