三角函数化简求值

题目

三角函数化简求值
cot10°-4cos10°=
4cos^2 35°-cos170°-tan160°sin170°=
（1+sin20°)/2sin20° -sin10°(cot5°-tan5°)

答案

1.ctg10－4cos10
=(cos10-4sin10cos10)/sin10
=(cos10-2sin20)/sin10
=(sin80-sin20-sin20)/sin10
=(2cos50sin30-sin20)/sin10
=(cos50-sin20)/sin10
=(sin40-sin20)/sin10
=2cos30sin10/sin10
=√3
2.原式=2(1+cos70)+cos10+tan20sin10
=2+2sin20+cos10+sin20sin10/cos20
=2+(2sin20cos20+(cos10cos20+sin20sin10))/cos20
=2+(sin40+cos10)/cos20
=2+(sin40+sin80)/cos20
=2+2sin60cos20/cos20
=2+根号3
3.