三角函数推导公式口诀

三角函数公式：正弦定理：a / sina = b / sinb = c / sinc；余弦定理：c² = a² + b² - 2abcosc；正切定理：tan(a/2) = (a - b) / (a + b) * cot(c/2)；倍角公式：sin(2a) = 2sinacosa；和差角公式：sin(a ± b) = sinacosb ± cosasinb；积化和差公式：sinacosb = (1/2)[sin(a + b) + sin(a - b)]。

三角函数推导公式口诀

正弦定理：

• a / sin(A) = b / sin(B) = c / sin(C)

余弦定理：

• c² = a² + b² - 2abcos(C)

正切定理：

• tan(A/2) = (a - b) / (a + b) * cot(C/2)

倍角公式：

• sin(2A) = 2sin(A)cos(A)
• cos(2A) = cos²(A) - sin²(A) = 1 - 2sin²(A)
• tan(2A) = (2tan(A)) / (1 - tan²(A))

半角公式：

• sin(A/2) = ±√((1 - cos(A)) / 2)
• cos(A/2) = ±√((1 + cos(A)) / 2)
• tan(A/2) = ±√((1 - cos(A)) / (1 + cos(A)))

和差角公式：

• sin(A ± B) = sin(A)cos(B) ± cos(A)sin(B)
• cos(A ± B) = cos(A)cos(B) ∓ sin(A)sin(B)
• tan(A ± B) = (tan(A) ± tan(B)) / (1 ∓ tan(A)tan(B))

积化和差公式：

• sin(A)cos(B) = (1/2)[sin(A + B) + sin(A - B)]
• cos(A)sin(B) = (1/2)[sin(A + B) - sin(A - B)]

和差化积公式：

• sin(A) + sin(B) = 2cos((A - B)/2)sin((A + B)/2)
• sin(A) - sin(B) = 2sin((A + B)/2)cos((A - B)/2)
• cos(A) + cos(B) = 2cos((A + B)/2)cos((A - B)/2)
• cos(A) - cos(B) = -2sin((A + B)/2)sin((A - B)/2)

辅助角公式：

• sin(A + π) = -sin(A)
• cos(A + π) = -cos(A)
• tan(A + π) = -tan(A)
• sin(A - π) = -sin(A)
• cos(A - π) = cos(A)
• tan(A - π) = -tan(A)

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