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:作业帮 分类:数学作业 时间:2024/10/06 12:44:36
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
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
=[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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