Question 965366
Find the exact value of the following under the given conditions. 
if tan(x)= -4/3 
and (pi/2)< x < pi 
and 
if sin(y)= 2/3 
and 0< y < (pi/2) 
find tan(x+y)
***
tanx=-4/3 ((3-4-5) reference right triangle in quadrant II)
sinx=4/5
cosx=-3/5
..
siny=2/3
cosy={{{sqrt(1-sin^2(y))=sqrt(1-4/9)=sqrt(5/9)=sqrt(5)/3}}}
..
sin(x+y)=sinx*cosy+cosx*siny=4/5*&#8730;5/3+-3/5*2/3=4&#8730;5/15-6/15=(4&#8730;5-6)/15
cos(x+y)=cosx*cosy-sinx*siny=-3/5*&#8730;5/3-4/5*2/3=-3&#8730;5/15-8/15=-(3&#8730;5+8)/15
tan(x+y)=sin(x+y)/cos(x+y)=-(4&#8730;5-6)/(3&#8730;5+8)
..
check:
tanx=-4/3 (Q2)
x=126.87&#730;
siny=2/3 (Q1)
y=41.81&#730;
x+y=168.68
tan(x+y)=tan(168.68)&#8776;-0.2002
exact value as computed above=-(4&#8730;5-6)/(3&#8730;5+8)&#8776;-0.2002