三角函数和差公式怎么推出来的

三角函数和差公式可从加减恒等式推导而来：和公式：sin(a + b) + sin(a - b) = 2sin(a)cos(b)cos(a + b) + cos(a - b) = 2cos(a)cos(b)差公式：sin(a + b) - sin(a - b) = 2cos(a)sin(b)cos(a + b) - cos(a - b) = -2sin(a)sin(b)

三角函数和差公式的推导

如何推导出三角函数和差公式？

三角函数和差公式可以从加减恒等式推导而来：

加减恒等式：

• sin(a + b) = sin(a)cos(b) + cos(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)
• cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

和差公式的推导：

和公式：

sin(a + b) + sin(a - b) = [sin(a)cos(b) + cos(a)sin(b)] + [sin(a)cos(b) - cos(a)sin(b)]= 2sin(a)cos(b)

cos(a + b) + cos(a - b) = [cos(a)cos(b) - sin(a)sin(b)] + [cos(a)cos(b) + sin(a)sin(b)]= 2cos(a)cos(b)

差公式：

sin(a + b) - sin(a - b) = [sin(a)cos(b) + cos(a)sin(b)] - [sin(a)cos(b) - cos(a)sin(b)]= 2cos(a)sin(b)

cos(a + b) - cos(a - b) = [cos(a)cos(b) - sin(a)sin(b)] - [cos(a)cos(b) + sin(a)sin(b)]= -2sin(a)sin(b)

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