Question

If sin A = 5/13, cos B = 3/5, and 0 < B < pi/2 < A < pi, what is cos (2A-B)?

Answer 1

sin A = 5/13
cos A = -12/13
tan A = -5/12

sin B = 4/5
cos B = 3/5
tan B = 4/3

Answer 2

cos 2A = (-12/13)^2 - (5/13)^2 = 119/169
sin 2A = (2)(5/13)(-12/13) = -120/169

Answer 3

cos(a+b) = cos(a) cos(b) - sin(a) sin(b)

Answer 4

cos (2A-B) = cos 2A cos B + sin 2A sin B

Answer 5

is that right?

Answer 6

yes

Answer 7

yes

Answer 8

therefore
cos (2A-B) = (119/169)(3/5) + (-120/169)(4/5) = -123/845

Answer 9

can the answer be negative?

Answer 10

definitely....
good job...:)

Answer 11

thanks!