How do you work this problem. I cannot find an example in the book to illustrate how to work it.

Question

Find the value of tan(a-b) if cos a=-3/5, sin b=5/13, 90<a<180, and 90<b<180

Thanks for any help

Answer 1

your text should have
tan(a-b) = (tan a - tan b)/(1 + tanatanb)
so you will need tan a and tan b

cos a = -3/5 and a is in the second quadrant, so by sketching a diagram it is easy to see that sin a = 4/5 and
tan a = - 4/3
similarly sin b = 5/13 and b is in quadrant II, so cos b = -12/13 and
tan b = -5/12
then tan(a-b)
=(-4/3 - (5/12))/(1 + (-4/3)(-5/12))
= -33/56