SOLUTION: a and b are positive acute angles. if sin a= 3/5 and cos b= 12/13, find the value of cos(a-b)

Question 846190: a and b are positive acute angles. if sin a= 3/5 and cos b= 12/13, find the value of cos(a-b)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
a and b are positive acute angles. if sin a= 3/5 and cos b= 12/13, find the value of cos(a-b)
***
Identity: cos(a-b)=cos a cos b+sin a sin b
..
sin a=3/5
cos a=4/5
cos b=12/13
sin b=5/13
..
cos(a-b)=4/5*12/13+3/5*5/13=48/65+15/65=63/65
..
calculator check:
sin a=3/5
a=36.87˚
..
cos b≈12/13
b≈22.62˚
..
a-b≈14.25˚
..
cos(a-b)≈cos(14.25)≈0.9692
exact ans:
cos(a-b)=63/65≈0.9692
RELATED QUESTIONS
If sin A = 3/5 and cos B = 12/13, and A and B are both positive acute angles, find the... (answered by ikleyn)

Given that A and B are acute angles such that sin A = 3/5 and cos B = 5/13, calculate the (answered by ikleyn)

If A and B are acute angles such that sin(A) = 3/5 and cos(B) = 5/13, find tan(A+B)... (answered by ikleyn)

For positive acute angles A and B, it is known that sin A = 35/37 and cos B = 5/13. Find... (answered by greenestamps)

If sin A=3/5, cos B=8/17, and A and B are acute angles, determine the exact value of tan... (answered by MathLover1,Solver92311)

If sinA=2/3 and CosB=3/5 and . Find Sin(A+B), Cos(A+B), tan(A+B), Where A, B and A+B... (answered by stanbon)

Angles A and B are located in the first quadrant. If sin A = 5/13 and cosB = 3/5,... (answered by Alan3354)

find the exact value of cos(a+B) if sin a= -4/5, and sin B=... (answered by Edwin McCravy)

If angle A and angle B are acute angles of right triangle ABC, what is the value of sin A (answered by jim_thompson5910)