SOLUTION: If sinA= -12/13, Q3, and cosB=4/5, Q1, calculate the exact value: a) sec (A-B) b) cot (A-B)

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Question 759397: If sinA= -12/13, Q3, and cosB=4/5, Q1, calculate the exact value:
a) sec (A-B)
b) cot (A-B)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If sinA= -12/13, Q3, and cosB=4/5, Q1, calculate the exact value:
a) sec (A-B)
b) cot (A-B)
***
sinA=-12/13
cosA=-5/13 (5-12-13 reference right triangle in Q3)
tanA=sin/cos=12/5
..
cosB=4/5
sinB=3/5 (3-4-5 reference right triangle in Q1)
tanB=sin/cos=3/4
..
Identity:cos%28A-B%29=cosAcosB%2BsinAsinB=-5%2F13%2A4%2F5-12%2F13%2A3%2F5=-20%2F65-36%2F65=-56%2F65
a) sec+%28A-B%29=1%2Fcos%28A-B%29=-65%2F56
..
Identity:
b) cot+%28A-B%29=1%2Ftan%28A-B%29=56%2F33
computer check:
sinA=-12/13
A≈67.38+180≈247.38º
cosB=4/5
B≈36.87º
A-B≈247.38-36.87≈210.51º
..
cos(A-B)=cos(210.51º)≈-0.8615
exact value=-56/65≈-0.8615
..
tan(A-B)=tan(210.51º)≈0.5892
exact value=33/56≈0.5892