化简:sin(a-pai/4)*sin(a+pai/4)
问题描述：
化简:sin(a-pai/4)*sin(a+pai/4)
答
pai-p 根号-g
sin(a-p/4)*sin(a+p/4)=(sinacosp/4-cosasinp/4)(sinacosp/4+cosasinp/4)=[g2/2(sina-cosa)][g2/2(sina+cosa)]=1/2(sina-cosa)(sina+cosa)=1/2(sin^2 a-cos^2 a)=1/2
答
sin(a-pai/4)*sin(a+pai/4)
=(1/2)[cos(a-pai/4-a-pai/4)-cos(a-pai/4+a+pai/4]
=(1/2)[cos(-pai/2)-cos(2a)]
=(1/2)(0-cos2a)
=-(cos2a)/2