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.

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