化简:2sin²2α+√3sin4α-(4tan2α/sin8α)·(1-tan²2α)/(1+tan²2α)化简:2sin²2α+√3sin4α-(4tan2α/sin8α)·(1-tan²2α)/(1+tan²2α)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 18:37:50
![化简:2sin²2α+√3sin4α-(4tan2α/sin8α)·(1-tan²2α)/(1+tan²2α)化简:2sin²2α+√3sin4α-(4tan2α/sin8α)·(1-tan²2α)/(1+tan²2α)](/uploads/image/z/8843758-70-8.jpg?t=%E5%8C%96%E7%AE%80%3A2sin%26%23178%3B2%CE%B1%2B%E2%88%9A3sin4%CE%B1-%EF%BC%884tan2%CE%B1%2Fsin8%CE%B1%EF%BC%89%C2%B7%281-tan%26%23178%3B2%CE%B1%29%2F%281%2Btan%26%23178%3B2%CE%B1%29%E5%8C%96%E7%AE%80%3A2sin%26%23178%3B2%CE%B1%2B%E2%88%9A3sin4%CE%B1-%EF%BC%884tan2%CE%B1%2Fsin8%CE%B1%EF%BC%89%C2%B7%281-tan%26%23178%3B2%CE%B1%29%2F%281%2Btan%26%23178%3B2%CE%B1%29)
化简:2sin²2α+√3sin4α-(4tan2α/sin8α)·(1-tan²2α)/(1+tan²2α)化简:2sin²2α+√3sin4α-(4tan2α/sin8α)·(1-tan²2α)/(1+tan²2α)
化简:2sin²2α+√3sin4α-(4tan2α/sin8α)·(1-tan²2α)/(1+tan²2α)
化简:2sin²2α+√3sin4α-(4tan2α/sin8α)·(1-tan²2α)/(1+tan²2α)
化简:2sin²2α+√3sin4α-(4tan2α/sin8α)·(1-tan²2α)/(1+tan²2α)化简:2sin²2α+√3sin4α-(4tan2α/sin8α)·(1-tan²2α)/(1+tan²2α)
首先2sin²2α=1-cos4α
而1-tan²2α=(cos²2α-sin²2α)/cos²2α=cos4α/cos²2α
1+tan²2α=1+sin²2α/cos²2α=1/cos²2α
所以
2sin²2α+√3sin4α- (4tan2α/sin8α)*(1-tan²2α)/(1+tan²2α)
=1-cos4α+√3sin4α -(4tan2α/sin8α)*cos4α
而sin8α=2sin4α*cos4α=4sin2α*cos2α*cos4α
故
(4tan2α/sin8α)*cos4α
=4sin2α *cos4α /(cos2α *4sin2α*cos2α*cos4α)
=1/cos²2α
那么
原式=1-cos4α+√3sin4α -1/cos²2α
= (cos²2α-1)/cos²2α +2*(√3/2 *sin4α -1/2 *cos4α)
= -tan²2α+2sin(4α-π/6)