Question

If tan A = 21/20 and cos B = 28/53 and angles A and B are in Quadrant I, find the valueof tan(A - B).

Answer 1

`\begin{gathered} \tan (A-B)=(\tan A-\tan B)/(1+\tan A\tan B) \\ \tan A=(21)/(20) \\ \text{tan B=?} \\ \text{cosB}=(28)/(53) \\ b=28 \\ h=53 \\ h^2=p^2+b^2 \\ p^2=53^2-28^2 \\ p^2=(53+28)(53-28) \\ p^2=81*25 \\ p=\sqrt[]{2025} \\ p=45 \\ \tan B=(45)/(28) \\ \tan (A-B)=((21)/(20)-(45)/(28))/(1+(45)/(28)*(21)/(20)) \\ =(1.05-1.607)/(1+1.05*1.607) \\ =-(0.557)/(2.687) \\ =-0.207 \end{gathered}`