Question

1+cos20°/sin20°-4sin10°tan80°=( )

请给出解析过程，谢谢

Answer 1

(1+cos20°）/sin20°]-4sin10°tan80°
=2cos²10°/(2sin10°cos10°)-4sin10°sin80°/cos80°
=cos10°/sin10°-4sin10°cos10°/sin10°
=cos10°/sin10°-2sin20°/sin10°
=（sin80º-2sin20°)/sin10°
=[(sin80°-sin20°)-sin20°]/sin10°
=[sin(50º+30º)-sin(50º-30º)-sin20°]/sin10°
=(2cos50°sin30°-sin20°)/sin10°
=(cos50°-sin20°)/sin10°
=(sin40°-sin20°)/sin10°
=[sin(30º+10º)-sin(30º-10º)]/sin10°
=(2cos30°sin10°)/sin10°
=2cos30°
=√3

若学习了和差化积公式更为方便
sinα-sinβ=2cos(α+β)/2sin(α-β)/2

Answer 2

原式=(1+2cos²10-1)/(4sin10cos10)-2cos80(sin80/cos80)
=cos10/(2sin10)-2sin80
=(cot10-4sin80)/4

追问

你好！你这个没做完啊