若1+(sinα)^2=3sinαcosα.求tanα.
来源:百度知道 编辑:UC知道 时间:2024/05/17 04:18:20
1+(sinα)^2=3sinαcosα
将 1=(sinα)^2+(cosα)^2 代入原方程中便得 2(sinα)^2+(cosα)^2=3sinαcosα
两边同时除以(cosα)^2得
2(tanα)^2-3tanα+1=0
=> (2tanα-1)(tanα-1)=0
tanα=1/2 或 tanα=1
1+(sinα)^2=3sinαcosα
两边除以(cosα)^2
1/(cosα)^2 +(tanα)^2=3tanα
(sec α)^2 +(tanα)^2-3tanα=0
1+(tan α)^2 +(tanα)^2-3tanα=0
1+2(tanα)^2-3tanα=0
(tanα-1)(2tanα-1)=0
tanα=1或者1/2
tanα=1/2或tana=1
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