作业帮(1/cos²80°-3/cos²10°)*1/cos20°=
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/06 09:42:09
(1/cos²80°-3/cos²10°)*1/cos20°=
(1/cos²80°-3/cos²10°)*1/cos20°=
(1/cos²80°-3/cos²10°)*1/cos20°=
[1/(cos80°)^2-3/(cos10°)^2]
*[1/cos20]
=[(1/cos80 + √3/cos10) * (1/cos80 - √3/cos10)] *[1/cos20]
=[(1/sin10 + √3/cos10) * (1/sin10 - √3/cos10)] *[1/cos20]
=[(cos10+√3sin10)/sin10cos10 * (cos10-√3sin10)/sin10cos10] *[1/cos20]
=[4sin40/sin20 * 4cos70/sin20] *[1/cos20]
=[16sin40/sin20] *[1/cos20]
=[32cos20] *[1/cos20]
=32