求X,x is in radians

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/10/05 03:50:33

求X,x is in radians
1）sin^2x- cosx =1
2）2sin^2-tanxcosx-1 =0

1）sin²x- cosx =1
1-cos²x-cosx=1
cosx(cosx+1)=0
cosx=0,cosx=-1
x=kπ+π/2,x=2kπ+π
2）2sin²x-tanxcosx-1 =0
2sin²x-(sinx/cosx)cosx-1=0
2sin²x-sinx-1=0
(2sinx+1)(sinx-1)=0
sinx=-1/2,sinx=1
sinx=1时x=2kπ+π/2
此时tanx无意义
所以sinx=-1/2
x=2kπ-5π/6,x=2kπ-π/6

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