请问怎么证明sinX+sin(X+Y)+sin(X+2Y)/cosX+cos(X+Y)+cos(X+

发布时间：2021-02-25 06:07:06

请问怎么证明sinX+sin(X+Y)+sin(X+2Y)/cosX+cos(X+Y)+cos(X+2Y)=tan(X+Y),

网友回答

sinX+sin(X+Y)+sin(X+2Y)/cosX+cos(X+Y)+cos(X+2Y)
=sinX+sin(X+2Y)+sin(X+Y)/cosX+cos(X+2Y)+cos(X+Y)
=2sin(X+X+2Y)/2cos(X-X-2Y)/2+sin(X+Y)/2cos(X+X+2Y)/2cos(X-X-2Y)/2+cos(X+Y)
=2sin(X+Y)cosY+sin(X+Y)/2cos(X+Y)cosY+cos(X+Y)
=sin(X+Y)(2cosY+1)/cos(X+Y)(2cosY+1)
=sin(X+Y)/cos(X+Y)
=tan(X+Y)
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