Question

设k∈Z,化简sin(-540°-α)-tan(180°-α)cos(kπ+α).

Answer 1

解析：原式=-sin(180°+α)+tanαcos(kπ+α)=sinα+tanαcos(kπ+α).

(ⅰ)当k=2n(n∈Z)时，

cos(kπ+α)=cos(2nπ+α)=cosα,

∴原式=sinα+tanαcosα=2sinα.

（ⅱ）当k=2n+1(n∈Z)时，

cos(kπ+α)=cos(π+α)=-cosα,

∴原式=sinα-tanαcosα=0.