化简{2sin50°+cos10°(1+(√3)tan10°)}/√(1-(sin^2)5°)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 19:16:52
化简{2sin50°+cos10°(1+(√3)tan10°)}/√(1-(sin^2)5°)

化简{2sin50°+cos10°(1+(√3)tan10°)}/√(1-(sin^2)5°)
化简{2sin50°+cos10°(1+(√3)tan10°)}/√(1-(sin^2)5°)

化简{2sin50°+cos10°(1+(√3)tan10°)}/√(1-(sin^2)5°)
2(√2)
原式={2sin50°+cos10°+√3sin10°}/cos5°
={2sin50°+2[1/2cos10°+√3/2sin10°]}/cos5°
={2sin50°+2[sin30°cos10°+cos30°sin10°}/cos5°
={2sin50°+2sin(30°+10°)}/cos5°
=2{sin50°+sin40°}/cos5°
=2√2{√2/2sin50°+√2/2cos50°}/cos5°
=2√2{cos45°sin50°+sin45°cos50°}/cos5°
=2√2{sin(45°+50°)}/cos5°
=2√2sin95°/cos5°
=2√2cos5°/cos5°
=2√2

2√2