The given expression is tan(A - B)
Since tan (A - B) is equal to

Since the values of cos A and sin B are

We will use the rules

csc B = 1/sin B, cot B = 1/tan B, sec A = 1/cos A

Substitute the value of csc B in rule (3) to find cot B
![\begin{gathered} \cot ^2B=((41)/(9))^2-1 \\ \cot ^2B=(1600)/(81) \\ \sqrt[]{\cot^2B}=\pm\sqrt[]{(1600)/(81)} \\ \cot B=(40)/(9) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/pd1pu3kcki8y2tyzcu3uk9dwp8flqljec9.png)
Reciprocal it to find tan B

Substitute the value of sec A in rule (2) to find tan A
![\begin{gathered} \tan ^2A=((37)/(35))^2-1 \\ \tan ^2A=(144)/(1225) \\ \sqrt[]{\tan^2A}=\pm\sqrt[]{(144)/(1225)} \\ \tan A=(12)/(35) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/mobmc0g8b47sqxlrvneol2ijpf8rqg9kgt.png)
Substitute the values of tan A and tan B in rule (1) above

The value of tan(A - B) is 165/1508