不用积化和差也行,不过思路是一致的.
分解 x = (x - π/6) + π/6
x-π/3 = (x - π/6) - π/6
所以原式 = cos[(x - π/6) + π/6] + cos[(x - π/6) - π/6] ,利用两角和(差)的余弦公式
= cos(x-π/6)*cos(π/6)- sin(x-π/6)*sin(π/6)+ cos(x-π/6)*cos(π/6)+ sin(x-π/6)*sin(π/6)
= 2*cos(x-π/6)*cos(π/6)
=2*m*(1/2) = m