已知θ是第三象限角,丨cosθ丨=m,sin(θ/2)+cos(θ/2)>0,则cos(θ/2)=?A.-根号下(1-m)/2 B.-根号下(1+m)/2 C.+/-根号下(1-m)/2D.根号下(1+m)/2

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已知θ是第三象限角,丨cosθ丨=m,sin(θ/2)+cos(θ/2)>0,则cos(θ/2)=?A.-根号下(1-m)/2 B.-根号下(1+m)/2 C.+/-根号下(1-m)/2D.根号下(1+m)/2

已知θ是第三象限角,丨cosθ丨=m,sin(θ/2)+cos(θ/2)>0,则cos(θ/2)=?A.-根号下(1-m)/2 B.-根号下(1+m)/2 C.+/-根号下(1-m)/2D.根号下(1+m)/2
已知θ是第三象限角,丨cosθ丨=m,sin(θ/2)+cos(θ/2)>0,则cos(θ/2)=?
A.-根号下(1-m)/2 B.-根号下(1+m)/2 C.+/-根号下(1-m)/2
D.根号下(1+m)/2

已知θ是第三象限角,丨cosθ丨=m,sin(θ/2)+cos(θ/2)>0,则cos(θ/2)=?A.-根号下(1-m)/2 B.-根号下(1+m)/2 C.+/-根号下(1-m)/2D.根号下(1+m)/2
θ是第三象限角,
丨cosθ丨=m, cosθ=-m
θ=2kπ+π+a
a ∈(0,π/2)
θ/2= kπ+π/2 +a/2
π/2 +a/2 ∈(π/2, 3π/4)
∵ sin(θ/2)+cos(θ/2)>0,
可以知道 θ/2 ∈ (2kπ-π/4, 2kπ+3π/4)
∴k 是偶数,设k为2n
θ/2= 2nπ+π/2 +a/2
第二象限角 cos(θ/2)小于0
cosθ=-m= 2cos²(θ/2)-1
cos(θ/2)= -√[ (1-m)/2]