SOLUTION: Find the exact value of the following given the conditions, I was able to find cos (A+B): {{{tanA= -7/24 }}} , {{{pi/2 < A < pi}}} ; {{{cosB= 5/6}}} {{{0 < B < pi/2}}} {{{sin(

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of the following given the conditions, I was able to find cos (A+B): {{{tanA= -7/24 }}} , {{{pi/2 < A < pi}}} ; {{{cosB= 5/6}}} {{{0 < B < pi/2}}} {{{sin(      Log On


   

Question 719842: Find the exact value of the following given the conditions, I was able to find cos (A+B):
tanA=+-7%2F24+ , pi%2F2+%3C+A+%3C+pi ; cosB=+5%2F6 0+%3C+B+%3C+pi%2F2
sin%28A%2BB%29
cos+%28A%2BB%29+=+%28-4%2F5%29+-%28%287sqrt%2811%29%29%2F150%29
sin%28A-B%29
tan%28A-B%29
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure how you can figure out cos(A-B) but not the others. You must have figured out sin(A), sin(B) and cos(A) to figure out cos(A-B). Just use these same values in the formulas:
sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
and
sin(A-B) = sin(A)cos(B) - cos(A)sin(B)

tan%28A-B%29+=+%28tan%28A%29-tan%28B%29%29%2F%281%2Btan%28A%29tan%28B%29%29
So we will need tan(A) and tan(B) to find tan(A-B). We were given tan(A). Using the same triangles you used to figure out the sin's and cos's of A and B we should be able to find tan(B):
tan%28B%29+=+sqrt%2811%29%2F5
Now just use these values in the tan(A-B) formula.