Question 850301
a and b are quadrant I angles with cos(a)= 15/17 and csc(b) = 41/9. find tan(a-b).
Identity: {{{tan(a-b)=(tana-tanb)/(1+tana*tanb)}}}
cosa=15/17
{{{sin(a)=sqrt(1-cos^2(a))=sqrt(1-(225/289))=sqrt(64/289)=8/17)}}}
tana=sin/cos=8/15
..
csc(b)=41/9
sin(b)=9/41
{{{cos(b)=sqrt(1-sin^2(b))=sqrt(1-(81/1681))=sqrt(1600/1681)=40/41)}}}
tanb=sin/cos=9/40
..
{{{tan(a-b)=(8/15-9/40)/(1+8/15*9/40)=185/672}}}
calculator check:
cos(a)=15/17
a≈28.072˚
sin(b)=9/41
b=12.680
a-b=15.392
tan(a-b)=tan(15.392)≈0.279
exact value=185/672≈0.279 (ans c.)