sin20°cos110°+cos160°sin70°要详细过程~~谢谢!

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 20:41:20
sin20°cos110°+cos160°sin70°要详细过程~~谢谢!

sin20°cos110°+cos160°sin70°要详细过程~~谢谢!
sin20°cos110°+cos160°sin70°
要详细过程~~谢谢!

sin20°cos110°+cos160°sin70°要详细过程~~谢谢!
sin20°cos110°+cos160°sin70°
=sin20°cos(180°-70°)+cos(180°-20°)sin70°
=-sin20°cos70°-cos20°sin70°
=-sin(20°+70°)
=-sin90°
=-1

cos110°= -sin20°, cos160°=-cos20°,sin70°= cos20°
sin20°cos110°+cos160°sin70°
= -(sin20°)^2-(cos20°)^2
= -[(sin20°)^2+(cos20°)^2]
= -1

sin20=cos70
cos110=-cos70
cos160=-cos20=-sin70
所以原式=-cos70*cos70-sin70*sin70=-1
结果为-1