三角函数计算最后一步的计算过程,越详细越好
3个回答
sin170 / (4*sin80*sin40/Sqrt[3]+cos170)
=sin10 / (4*cos10*sin40/Sqrt[3]-cos10)
=2*sin10*cos10 / (2*(cos10)^2*(4*sin40/Sqrt[3]-1))
=sin20 / ((cos20+1)*(4*sin40/Sqrt[3]-1))
往证分母=cos20.
(cos20+1)*(4*sin40/Sqrt[3]-1)
=4/Sqrt[3] * cos20*sin40+4/Sqrt[3] * sin40 - cos20-1
=2/Sqrt[3] * (sin60+sin20)+4/Sqrt[3] * sin40 - cos20-1
=2/Sqrt[3] * sin20 + 4/Sqrt[3] * sin40 - cos20
=2/Sqrt[3] * sin20 + 4/Sqrt[3] * (sin60*cos20-cos60*sin20) - cos20
=2/Sqrt[3] * sin20 + 2cos20 - 2/Sqrt[3] * sin20 - cos20
=cos20
