Question

化简cos^2(a+15)+sin^2(a-15))+sin(a+180)cos(a-180)

Answer 1

余弦二倍角公式：Cos2a=1-2Sina^2=2Cosa^2-1

正弦二倍角公式：sin2α = 2cosαsinα

所以

[2sinacos15°]*[2cosa*sin(-15°)]

=(2sinacosa)*(-2sin15°cos15°)

=-sin2asin30°

=-(1/2)*sin2a

看不懂是因为,你给出的解题过程有省略,详细如下：

cos^2(a+15)+sin^2(a-15)+sin(a+180)cos(a-180)

=cos^2(a+15)+sin^2(a+15)-sin^2(a+15)+sin^2(a-15)+sinacosa

=1+[sin^2(a-15)-sin^2(a+15)]+sinacosa

=1+[sin(a-15)+sin(a+15)][sin(a-15)-sin(a+15)]+sinacosa

=1+[2sinacos15]*[2cosa*sin(-15)]+sinacosa

=1-sin2a*sin30+(1/2)*sin2a

=1-(1/2)*sin2a+(1/2)*sin2a

=1