Question

化简sin(nπ+2π/3)×cos(nπ+4π/3) n属于Z 高中数学

谁来教下啊 在线等 要详细步骤！！！！ 谢谢

Answer 1

解：①当n=2k，k∈Z时，sin(nπ+2π/3)·cos(nπ+4π/3)= sin(2π/3)·cos(4π/3)= sin(π-π/3)·cos(π+π/3)= sin(π/3)·[-cos(π/3)]=-√3/4②当n=2k+1，k∈Z时，sin(nπ+2π/3)·cos(nπ+4π/3)= sin(π+2π/3)·cos(π+4π/3)= sin(2π/3)·cos(4π/3)= sin(π-π/3)·cos(π+π/3)= sin(π/3)·[-cos(π/3)]=-√3/4 故：sin(nπ+2π/3)·cos(nπ+4π/3) =-√3/4