化简:cos(4n+1/4π+α)+cos(4n−14π-α),n∈z.
问题描述:
化简:cos(
π+α)+cos(4n+1 4
π-α),n∈z. 4n−1 4
答
cos(
π+α)+cos(4n+1 4
π-α)4n−1 4
=cos(nπ+
+α)+cos(nπ−π 4
-α).π 4
当n为偶数时,
原式=cos(
+α)+cos(π 4
+α)π 4
=2cos(
+α);π 4
当n为奇数时,
原式=-cos(
+α)-cos(π 4
+α)π 4
=-2cos(
+α).π 4