问题 填空题
化简
1+2sin290°cos430°
sin250°+cos790°
=______.
答案

原式=

1+2sin(360°-70°)cos(360°+70°)
sin(180°+70°)+cos(720°+70°)

=

1-2sin70°cos70°
-sin70°+cos70°
=
|sin70°-cos70°|
-sin70°+cos70°
=
sin70°-cos70°
-(sin70°-cos70°)
=-1.

故答案为:-1

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