一道必修四数学题2sin50°+sin80°(1+根号3 tan10°)-----------------------------根号1+cos10°求值题.
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/29 02:52:48
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一道必修四数学题2sin50°+sin80°(1+根号3 tan10°)-----------------------------根号1+cos10°求值题.
一道必修四数学题
2sin50°+sin80°(1+根号3 tan10°)
-----------------------------
根号1+cos10°
求值题.
一道必修四数学题2sin50°+sin80°(1+根号3 tan10°)-----------------------------根号1+cos10°求值题.
先化简分子:
2sin50°+sin80°(1+√3 tan10°)
=2sin50°+sin80°*[(cos10°+√3 sin10°)/cos10°]
=2sin50°+sin80°*[2(cos60°cos10°+sin60°sin10°)/cos10°]
=2sin50°+cos10°*(2cos50°/cos10°)
=2sin50°+2cos50°
=2(sin50°+cos50°)
=2(sin40°+cos40°)
再化简分母:
1+cos10°
=1+sin80
=sin²40°+2sin40°cos40°+cos²40°
=(sin40°+cos40°)²
故√(1+cos10° )
=√(sin40°+cos40°)²
=sin40°+cos40°
故原式=2(sin40°+cos40°)/sin40°+cos40°
=2
计算器的答案是
1.53