设a是第二象限角,且cosa/2=-1/2,那么(根号下1-singa)/(cosa/2-sina/2)的值是A;-1B;1/2C;1D;2

Question

设a是第二象限角,且cosa/2=-1/2,那么(根号下1-singa)/(cosa/2-sina/2)的值是 A;-1 B;1/2 C;1 D;2

Answer 1

a是第二象限角,cosa(0)=√[1-(cosa)^2]=√3/2
√3/2=sina=2sin(a/2)cos(a/2)=2*sin(a/2)*(-1/2),得sin(a/2)=-√3/2
√(1-sina)/[cos(a/2)-sin(a/2)]
=√[1-2sin(a/2)cos(a/2)]/[cos(a/2)-sin(a/2)]
=√{[sin(a/2)]^2+[cos(a/2)]^2-2sin(a/2)cos(a/2)}/[cos(a/2)-sin(a/2)]
=√[cos(a/2)-sin(a/2)]^2/[cos(a/2)-sin(a/2)]//////cos(a/2)-sin(a/2)>0
=1