Question

Cosx=-1/3 x belongs third quadrant find sin x/2 cosx/2 tanx/2

Answer 1

Step-by-step explanation:

since x is in III quadrent

180°<x<270°

devide 2 all sides

180°/2<x/2<270°/2

90°<x<135°

x lies in II quadrent

given cosx=-1/3

1+cos2x=2cos²x

and,1-cos2x=2sin²x

so,1+cosx=1+cos(2.2/x)

1+cosx=2cos²x/2

(1+cosx)/2=cos²x/2

lly,(1-cosx)/2=sin²x/2

sin²x/2=(1-cosx)/2

sinx/2 =√(1+1/3)/2

=√4/6

=2/√6×√6/√6

=2√6/6

=√6/3

cos²x/2=(1+cosx))2

cosx/2=√(1-1/3)/2

=√2/6

=√1/3×√3/√3

=√3/3

x lies in II quadrent

cosx/2=-√3/3

tanx/2=(sinx/2)/(cosx/2)

=√6/3×(3/√3)

=√2

x lies in II Quadrant

tanx/2=-√2