Answer:
[tex]A - B = 135 \degree[/tex]
Step-by-step explanation:
Recall the trigonometric identity:
[tex]\tan(A - B)=\frac{\tan A-\tan B}{1+\tan A \tan B}[/tex]
We substitute;
tan A=-1/7 and tan B=3/4
[tex]\tan(A - B)=\frac{ - \frac{1}{7} - \frac{3}{4} }{1 - \frac{1}{7} \times \frac{3}{4} }[/tex]
[tex]\tan(A - B) = - 1[/tex]
This implies that,
[tex]A - B = { \tan}^{ - 1} ( - 1)[/tex]
[tex]A - B = { \tan}^{ - 1} ( 1) + 90[/tex]
[tex]A - B = 45+ 90[/tex]
[tex]A - B = 135 \degree[/tex]
