Question

If tan A = 4/3 and tan Band tan B= 12/5calculate and simplify the following:tan (A - B) =

Answer 1

There are some relations between the trigonometric functions. Tan(A-B) is only one of them and it is expressed by the following:

`\begin{gathered} \tan (A-B)=((\tan A-\tan B))/((1+(\tan A)\cdot(\tan B))) \\ \tan (A-B)=(((4)/(3)-(12)/(5)))/((1+((4)/(3))\cdot((12)/(5)))) \end{gathered}`

So, to get the answer we just solve the arithmetic operations as following:

`\begin{gathered} \tan (A-B)=(((20-36)/(15)))/((1+((48)/(15)))) \\ \tan (A-B)=(((-16)/(15)))/(((5)/(5)+((16)/(5)))) \\ \tan (A-B)=((-16)/(15))/((21)/(5)) \\ \tan (A-B)=(-16\cdot5)/(15\cdot21) \\ \tan (A-B)=(-80)/(315) \\ \tan (A-B)=-(16)/(63) \end{gathered}`