Question

如何化简cos(x)- sin(x)？

Answer 1

要化简cos(x) - sin(x)，可以使用三角函数的和差公式来简化：
cos(x) - sin(x) = cos(x) - (sin(x)*cos(π/2) + cos(x)*sin(π/2))
= cos(x) - sin(x)*cos(π/2) - cos(x)*sin(π/2)
= cos(x) - cos(π/2)*sin(x) - sin(π/2)*cos(x)
= cos(x) - cos(x)*sin(π/2) - sin(x)*cos(π/2)
= cos(x) - cos(x) - sin(x)
= -sin(x)
所以，cos(x) - sin(x)可以化源誉郑简为-sin(x)。
同样地，要化简sin(x) - cos(x)，也可以使用三雹颂角函数的和差公式：
sin(x) - cos(x) = sin(x) - (sin(x)*cos(π/2) + cos(x)*sin(π/2))
= sin(x) - sin(x)*cos(π/2) - cos(x)*sin(π/2)
= sin(x) - cos(π/2)*sin(x) - sin(π/2)*cos(x)
= sin(x) - sin(x)*cos(π/2) - cos(x)*sin(π/2)
= sin(x) - sin(x) - cos(x)
= -cos(x)
因此，sin(x) - cos(x)可以化虚蔽简为-cos(x)。