1. 正弦（sin）和余弦（cos）：
– sin(x) = 对边/斜边
– cos(x) = 邻边/斜边
– sin(x + π/2) = cos(x)
– cos(x + π/2) = -sin(x)
– sin(x – π/2) = -cos(x)
– cos(x – π/2) = sin(x)
2. 正切（tan）和余切（cot）：
– tan(x) = sin(x) / cos(x)
– cot(x) = cos(x) / sin(x)
– tan(x + π/2) = cot(x)
– cot(x + π/2) = -tan(x)
– tan(x – π/2) = -cot(x)
– cot(x – π/2) = tan(x)
3. 正割（sec）和余割（csc）：
– sec(x) = 1 / sin(x)
– csc(x) = 1 / cos(x)
– sec(x + π/2) = 1 / sin(x)
– csc(x + π/2) = 1 / cos(x)
– sec(x – π/2) = 1 / sin(x)
– csc(x – π/2) = 1 / cos(x)
4. 余割（csc）和余正割（cosec）：
– csc(x) = 1 / sin(x)
– cosec(x) = 1 / cos(x)
– csc(x + π/2) = 1 / sin(x)
– cosec(x + π/2) = 1 / cos(x)
– csc(x – π/2) = 1 / sin(x)
– cosec(x – π/2) = 1 / cos(x)
5. 双角公式：
– sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
– cos(a + b) = cos(a)cos(b) – sin(a)sin(b)
– sin(a – b) = sin(a)cos(b) – cos(a)sin(b)
– cos(a – b) = cos(a)cos(b) + sin(a)sin(b)
6. 倍角公式：
– sin(2x) = 2 sin(x) sin(x)
– cos(2x) = 2 cos(x) cos(x)
– tan(2x) = 2 tan(x) tan(x)
– sec^2(2x) = 1 / (1 + tan^2(x))
– csc^2(2x) = 1 / (1 + cos^2(x))
– sec^2(2x) = 1 / (1 + tan^2(x))
– csc^2(2x) = 1 / (1 + cos^2(x))
7. 半角公式：
– sin^2(x/2) = 1 – cos^2(x/2)
– cos^2(x/2) = 1 – sin^2(x/2)
– tan^2(x/2) = 1 – cos^2(x/2)
– sec^2(x/2) = 1 – tan^2(x/2)
– csc^2(x/2) = 1 – sec^2(x/2)
– sec^2(x/2) = 1 – tan^2(x/2)
– csc^2(x/2) = 1 – sec^2(x/2)
8. 半角和差公式：
– sin(x/2 + y/2) = sin(x/2)cos(y/2) + cos(x/2)sin(y/2)
– cos(x/2 + y/2) = cos(x/2)cos(y/2) – sin(x/2)sin(y/2)
– sin(x/2 – y/2) = sin(x/2)cos(y/2) – cos(x/2)sin(y/2)
– cos(x/2 – y/2) = cos(x/2)cos(y/2) + sin(x/2)sin(y/2)
9. 半角和差公式的逆用：
– sin(x/2 + y/2) = sin((x + y)/2)
– cos(x/2 + y/2) = cos((x + y)/2)
– sin(x/2 – y/2) = sin((x – y)/2)
– cos(x/2 – y/2) = cos((x – y)/2)
10. 二倍角公式：
– sin(2x + 3t) = 2 sin(x + t) cos(3t)
– cos(2x + 3t) = 2 cos(x + t) sin(3t)
– tan(2x + 3t) = 2 tan(x + t) tan(3t)
– sec^2(2x + 3t) = 1 / (1 + tan^2(x + t))
– csc^2(2x + 3t) = 1 / (1 + cos^2(x + t))
– sec^2(2x + 3t) = 1 / (1 + tan^2(x + t))
– csc^2(2x + 3t) = 1 / (1 + cos^2(x + t))
11. 二倍角和差公式：
– sin(2x + y) = sin(x + y)cos(2t) – cos(x + y)sin(2t)
– cos(2x + y) = cos(x + y)cos(2t) + sin(x + y)sin(2t)
– tan(2x + y) = tan(x + y)cos(2t) + sec^2(x + y)sin(2t)
– sec^2(2x + y) = 1 / (1 + tan^2(x + y))
– csc^2(2x + y) = 1 / (1 + cos^2(x + y))
– sec^2(2x + y) = 1 / (1 + tan^2(x + y))
– csc^2(2x + y) = 1 / (1 + cos^2(x + y))
12. 二倍角和差公式的逆用：
– sin(2x + y) = sin((x + y)/2)cos((2t)/2) – cos((x + y)/2)sin((2t)/2)
– cos(2x + y) = cos((x + y)/2)cos((2t)/2) + sin((x + y)/2)sin((2t)/2)
– tan(2x + y) = tan((x + y)/2)cos((2t)/2) + sec^2((x + y)/2)sin((2t)/2)
– sec^2(2x + y) = 1 / (1 + tan^2((x + y)/2))
– csc^2(2x + y) = 1 / (1 + cos^2((x + y)/2))
– sec^2(2x + y) = 1 / (1 + tan^2((x + y)/2))
– csc^2(2x + y) = 1 / (1 + cos^2((x + y)/2))
通过练习这些基本公式，你可以逐渐提高解题速度和准确性。记住，理解每个公式背后的几何意义也是非常重要的。随着实践的增加，你会发现自己在解决三角学问题时越来越得心应手。