若θ是第二象限角,cos(θ/2)-sin(θ/2)=√(1-sinθ)则角θ/2所在的象限是

Question

若θ是第二象限角,cos(θ/2)-sin(θ/2)=√(1-sinθ)则角θ/2所在的象限是______

Answer 1

cos(θ/2)-sin(θ/2)=√(1-sinθ)
得：
cos(θ/2)-sin(θ/2) = |cos(θ/2)-sin(θ/2)|
实际上就是：cos(θ/2)>sin(θ/2)
说明在直线y = x 下方即一,三,四
又θ在二象限,则π/4+kπ < θ/2 < π/2+kπ
即第三象限,且在y = x 下方