Please can you show all the work not just answer i have post

Solution

given tana=8/15 , 180^o<a<270^o

=>90^o<a/2<135^o

tana=8/15

=>cosa=-15/[8²+15²]=-15/17

=>sina=-8/[8²+15²]=-8/17

cos(a/2)=-[(1+cosa)/2]

cos(a/2)=-[(1+(-15/17))/2]

cos(a/2)=-(1/17)

sin(a/2)=[(1-cosa)/2]

sin(a/2)=[(1-(-15/17))/2]

sin(a/2)=(16/17)

tan(a/2)=sin(a/2) /cos(a/2)

tan(a/2)=((16/17)) /(-(1/17))

tan(a/2)=-16

tan(a/2)=-4