化简：[cos(a+15度)]^2+[sin(a-15度)]^2+[sin(a+180度)]*[cos(a-180度)]

来源：学生作业帮编辑：搜搜做题作业网作业帮分类：数学作业时间：2024/06/14 08:50:10

化简：[cos(a+15度)]^2+[sin(a-15度)]^2+[sin(a+180度)]*[cos(a-180度)].
请大家解释一下.
[cos(a+15度)]^2+[sin(a-15度)]^2+[sin(a+180度)]*[cos(a-180度)]
=[cos(2a+30)+1]/2+[1-cos（2a-30)]/2+1/2sin2a
=1+[cos(2a+30)-cos(2a-30)]/2+1/2sin2a
=1-2sin2a*sin30/2+1/2sin2a
=1
第一步有点看不懂用的是什么公式啊

[cos(a+15度)]^2+[sin(a-15度)]^2+[sin(a+180度)]*[cos(a-180度)]
=[cos(2a+30)+1]/2+[1-cos（2a-30)]/2+1/2sin2a（倍角公式）
=1+[cos(2a+30)-cos(2a-30)]/2+1/2sin2a
=1-2sin2a*sin30/2+1/2sin2a
=1
sin(a+180度)cos(a-180度)
= [sin(a+180度+a-180度)+sin(a+180度-a+180度)]/2
=[sin2a+sin360]/2
=1/2sin2a

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