Question

If csc A= -5/3 and csc B = -13/5 with angle A and angle B in quadrant 3. What is value of cos(A-B)?

Answer 1

`cos(A-B)=63/65`.

Explanation:

We start by taking note that angles `A and B` are in `Q_(III`, so that, `cosA and cosB` both will be `-ve`.

`cscA=-5/3rArrsinA=-3/5rArrcosA=-sqrt(1-sin^2A)=-sqrt(1-9/25)=-sqrt16/25=-4/5`

Similarly, `cscB=-13/5rArrcosB=-12/13`

Therefore, reqd. value`=cos(A-B)=cosAcosB+sinAsinB`

`=(-4/5)(-12/13)+(-3/5)(-5/13)`

`48/65+15/65=63/65`.