化简(2sin50+sin10(1+根号3tan10))根号(2sin^280)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/13 22:25:20
化简(2sin50+sin10(1+根号3tan10))根号(2sin^280)
原式=[ 2sin50°+sin10°(1+√3·tan10°)]√2cos10°
=2√2sin50°cos10°+√2 sin10°cos10°+√6 sin^210°
=2√2sin50°cos10°+√2/2 sin20°+√6/2(1-cos20°)
=2√2sin50°cos10°+√2/2 sin20°-√6/2cos20°+√6/2
=2√2sin50°cos10°-√2(√3/2cos20°-1/2sin20°)+√6/2
=2√2sin50°cos10°-√2sin(60°-20°)+√6/2
=2√2sin50°cos10°-√2sin40°+√6/2
=2√2sin50°cos10°-√2sin(50°-10°)+√6/2
=2√2sin50°cos10°-√2sin50°cos10°+√2cos50°sin10°+√6/2
=√2sin50°cos10°+√2cos50°sin10°+√6/2
=√2sin60°+√6/2
=√6
再问: sin^2(80)怎么变成cos10了
再答: sin80=sin(90-10)=cos10 √sin^2(80)=cos10
=2√2sin50°cos10°+√2 sin10°cos10°+√6 sin^210°
=2√2sin50°cos10°+√2/2 sin20°+√6/2(1-cos20°)
=2√2sin50°cos10°+√2/2 sin20°-√6/2cos20°+√6/2
=2√2sin50°cos10°-√2(√3/2cos20°-1/2sin20°)+√6/2
=2√2sin50°cos10°-√2sin(60°-20°)+√6/2
=2√2sin50°cos10°-√2sin40°+√6/2
=2√2sin50°cos10°-√2sin(50°-10°)+√6/2
=2√2sin50°cos10°-√2sin50°cos10°+√2cos50°sin10°+√6/2
=√2sin50°cos10°+√2cos50°sin10°+√6/2
=√2sin60°+√6/2
=√6
再问: sin^2(80)怎么变成cos10了
再答: sin80=sin(90-10)=cos10 √sin^2(80)=cos10
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