SOLUTION: FInd the exact value of tan(A-B) if cos(A)=3/5 where 0< or equal to A <or equal to pie/2 and sin(B)=(-5/13) where pie< or equal to B < or equal to 3pie/2

Algebra ->  Inequalities -> SOLUTION: FInd the exact value of tan(A-B) if cos(A)=3/5 where 0< or equal to A <or equal to pie/2 and sin(B)=(-5/13) where pie< or equal to B < or equal to 3pie/2      Log On


   

Question 882514: FInd the exact value of tan(A-B) if cos(A)=3/5 where 0< or equal to A
Answer by lwsshak3(11628) About Me  (Show Source):
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FInd the exact value of tan(A-B) if cos(A)=3/5 where 0< or equal to A ***
cos A=3/5 (working with a (3-4-5) reference right triangle in quadrant I)
sinA=4/5
..
sinB=-5/13 (working with a (5-12-13) reference right triangle in quadrant III)
cosB=-12/13
..
(sin(A-B)=sinAcosB-cosAsinB=4/5*(-12/13)-3/5*(-5/13)=-48/65+15/65=-33/65
cos(A-B)=cosAcosB+sinAsinB=3/5*(-12/13)+4/5*(-5/13)=-36/65-20/65=56/65
tan(A+B)=sin(A+B)/cos(A+B)=-33/56