Question

4cos50°-tan40°等于多少？过程！

Answer 1

根号3，利用sinθ+sinφ = 2 sin[(θ+φ)/2] cos[(θ-φ)/2]和sinθ-sinφ = 2 cos[(θ+φ)/2] sin[(θ-φ)/2]
这两个公式，原式=4cos50-cot50=(4cos50sin50-cos50)/sin50=(2sin100-cos50)/sin50=(sin80+sin80-sin40)/sin50=(sin80+2cos60sin20)/sin50=(sin80+sin20)/sin50=2sin50cos30/sin50=2cos30=根号3 不懂再联系

Answer 2

4cos50º-tan40º
=4sin40º-sin40º/cos40º
=(4sin40°cos40°-sin40°)/cos40°
=(2sin80°-sin40°)/cos40°
=[2cos10°-sin(30°+10°)]/cos40°
=(2cos10°-1/2cos30°-√3/2sin10°)/cos40°
=(3/2cos10°-√3/2sin10°)/cos40°
=√3(√3/2cos10°-1/2sin10°)/cos40°
=√3（cos30°cos10°-sin30°sin10°)/cos40°
=√3cos40°/cos40°
=√3

Answer 3

4cos50°-tan40°=4sin40°-sin40°/cos40°
=(2sin80°-sin40°)/cos40°
=(2cos10°-sin40°)/cos40°
=[2cos(40°-30°)-sin40°]/cos40°
=[√3cos40°+sin40°-sin40°]/cos40°
=√3cos40°/cos40°
=√3