Question

cosx- sinx=√2* sin(x-π/4)的推导过程

Answer 1

cosx - sinx = √2 * sin(x - π/4)
推导过程:
根据三角函数的基本公式:
cos(x - π/4) = cosx * cos(π/4) + sinx * sin(π/4)
sin(x - π/4) = sinx * cos(π/4) - cosx * sin(π/4)
其中:
cos(π/4) = sin(π/4) = √2/2
将这些值代入上面两个公式,可得:
cos(x - π/4) = √2/2 * (cosx + sinx)
sin(x - π/4) = √2/2 * (sinx - cosx)
将两式相减可得:
cosx - sinx = √2 * sin(x - π/4)
因此,cosx - sinx = √2 * sin(x - π/4)。这个结论很好地体现了三角函数之间的转换关系