化简:sin7°+cos15°sin8°cos7°−sin15°sin8°
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/11/17 09:00:57
化简:
sin7°+cos15°sin8° |
cos7°−sin15°sin8° |
因为cos15°sin8°=
1
2[sin(8°+15°)+sin(8°-15°)=
1
2(sin23°-sin7°)],
sin15°sin8°=
1
2(cos7°-cos23°),
所以
sin7°+cos15°sin8°
cos7°−sin15°sin8°=
sin23°+sin7°
cos23°+cos7°
=
2sin15°cos8°
2cos15°cos8°=tan15°=tan(45°-30°)
=
tan45°−tan30°
1+tan45°tan30°=2-
3.
1
2[sin(8°+15°)+sin(8°-15°)=
1
2(sin23°-sin7°)],
sin15°sin8°=
1
2(cos7°-cos23°),
所以
sin7°+cos15°sin8°
cos7°−sin15°sin8°=
sin23°+sin7°
cos23°+cos7°
=
2sin15°cos8°
2cos15°cos8°=tan15°=tan(45°-30°)
=
tan45°−tan30°
1+tan45°tan30°=2-
3.
1.sin7°+cos15°sin8°/cos7°-sin15°cos8°=
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