Answer:
-3
Explanation:
Remember the following:
cos(x)=cos(x/2 + x/2) = cos(x/2)*cos(x/2) -sin(x/2)*sin(x/2)
cos(x)=cos2(x/2) - sin2(x/2)
We also know that sin2(a)+cos2(a)=1,
so sin2(x/2)=1 - cos2(x/2). obtained from previous step.
So, our first expression can be written as:
cos(x)=cos2(x/2)-1+cos2(x/2)
Where we obtain that: cos(x/2)= sqrt( 1+ cos(x))/ sqrt(2)
If we again use sin2(a)+cos2(a)=1, we will obtain the following relation:
sin(x/2)= sqrt(1-cos(x))/sqrt(2)
Next Tang(x/2)= sin(x/2) / cos(x/2)= sqrt(1-cos(x))/sqrt(1+cos(x))=
SQRT(9/1)=3
In the given range, cos(x), hence tan(x/2) is also negative