sin10°=a,3/sin²40°-1/cos²40°的值
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/29 11:22:06
sin10°=a,3/sin²40°-1/cos²40°的值
3/sin²40°-1/cos²40°=(3cos²40°-sin²40°)/sin²40°cos²40°
=4(√3cos40°+sin40°)(√3cos40°-sin40°)/sin²80°
=32((√3/2cos40°+1/2sin40°)(√3/2cos40°-1/2sin40°)/2sin²80°
=32sin(60°+40°)sin(60°-40°)/(1-cos160°)
=32sin100°sin20°/(1+cos20°)
=64cos²10°sin10°/(2cos²10°)
=32sin10°
=32a
=4(√3cos40°+sin40°)(√3cos40°-sin40°)/sin²80°
=32((√3/2cos40°+1/2sin40°)(√3/2cos40°-1/2sin40°)/2sin²80°
=32sin(60°+40°)sin(60°-40°)/(1-cos160°)
=32sin100°sin20°/(1+cos20°)
=64cos²10°sin10°/(2cos²10°)
=32sin10°
=32a
求sin²10°+cos²40°+sin10°cos40°的值
不查表求值sin²10°+cos²40°+sin10°cos40° 请有具体的解题过程,
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