用加法定理求下列函数值:1、sin105°；2、cos75°；3、sin(-23π/12).

Question

用加法定理求下列函数值:1、sin105°；2、cos75°；3、sin(-23π/12).

Answer 1

：（1）sin105°
=sin(60°+45°)=sin60°cos45°+cos60°sin45°
=(√3/2)(√2/2)+(1/2)(√2/2)
=(√6+√2)/4,
（2）cos75°
=cos(30°+45°)=cos30°cos45°-sin30°sin45°
=(√3/2)(√2/2)-(1/2)(√2/2)
=(√6-√2)/4,
（3）sin(-23π/12)
=sin(-2π+π/12)=sin(π/12)=sin(π/3-π/4)
=sin(π/3)cos(π/4)-cos(π/3)sin(π/4)
=(√3/2)(√2/2)-(1/2)(√2/2)
=(√6-√2)/4