计算:sin30+sin(30+120)+sin(30+240),sin60+sin(60+120)+sin(60+240)观察以上两式极其结果的特点,请写出一个一般的等式,使得上述的两式为它的一个特例,并证明你写的结论.我算得都为0,结果:s
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![计算:sin30+sin(30+120)+sin(30+240),sin60+sin(60+120)+sin(60+240)观察以上两式极其结果的特点,请写出一个一般的等式,使得上述的两式为它的一个特例,并证明你写的结论.我算得都为0,结果:s](/uploads/image/z/8600201-17-1.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9Asin30%2Bsin%EF%BC%8830%2B120%EF%BC%89%2Bsin%EF%BC%8830%2B240%EF%BC%89%2Csin60%2Bsin%EF%BC%8860%2B120%EF%BC%89%2Bsin%EF%BC%8860%2B240%EF%BC%89%E8%A7%82%E5%AF%9F%E4%BB%A5%E4%B8%8A%E4%B8%A4%E5%BC%8F%E6%9E%81%E5%85%B6%E7%BB%93%E6%9E%9C%E7%9A%84%E7%89%B9%E7%82%B9%2C%E8%AF%B7%E5%86%99%E5%87%BA%E4%B8%80%E4%B8%AA%E4%B8%80%E8%88%AC%E7%9A%84%E7%AD%89%E5%BC%8F%2C%E4%BD%BF%E5%BE%97%E4%B8%8A%E8%BF%B0%E7%9A%84%E4%B8%A4%E5%BC%8F%E4%B8%BA%E5%AE%83%E7%9A%84%E4%B8%80%E4%B8%AA%E7%89%B9%E4%BE%8B%2C%E5%B9%B6%E8%AF%81%E6%98%8E%E4%BD%A0%E5%86%99%E7%9A%84%E7%BB%93%E8%AE%BA.%E6%88%91%E7%AE%97%E5%BE%97%E9%83%BD%E4%B8%BA0%2C%E7%BB%93%E6%9E%9C%EF%BC%9As)
计算:sin30+sin(30+120)+sin(30+240),sin60+sin(60+120)+sin(60+240)观察以上两式极其结果的特点,请写出一个一般的等式,使得上述的两式为它的一个特例,并证明你写的结论.我算得都为0,结果:s
计算:sin30+sin(30+120)+sin(30+240),sin60+sin(60+120)+sin(60+240)
观察以上两式极其结果的特点,请写出一个一般的等式,使得上述的两式为它的一个特例,并证明你写的结论.
我算得都为0,结果:sina+sin(a+120)+sin(a+120).要怎么证明呢?
计算:sin30+sin(30+120)+sin(30+240),sin60+sin(60+120)+sin(60+240)观察以上两式极其结果的特点,请写出一个一般的等式,使得上述的两式为它的一个特例,并证明你写的结论.我算得都为0,结果:s
sina+sin(a+120)+sin(a+240)
=sina+sinacos120+cosasin120+sinacos240+cosasin240
=sina-1/2*sina+√3/2*cosx-1/2*sina-√3/2*cosx
=0
(1-2x+x^2)/x√x
=(1-2x+x^2)*x^(-3/2)
=x^(-3/2)-2x^(-1/2)+x^(1/2)
所以就是幂函数求积分
原式=x^(-3/2+1)/(-3/2+1)-2x^(-1/2+1)/(-1/2+1)+x^(1/2+1)/(1/2+1)+C
=-2x^(-1/2)-4x^(1/2)+2x^(3/2)/3+C
=-2/√x-4√x+2x√x/3+C