Question

if tanA= -1/7 and tanB= 3/4, where A is abtuse and B is acute, Find without using tables the value of A-B (ans/135)​

Answer 1

Answer:

$A - B = 135 \degree$

Step-by-step explanation:

Recall the trigonometric identity:

$\tan(A - B)=\frac{\tan A-\tan B}{1+\tan A \tan B}$

We substitute;

tan A=-1/7 and tan B=3/4

$\tan(A - B)=\frac{ - \frac{1}{7} - \frac{3}{4} }{1 - \frac{1}{7} \times \frac{3}{4} }$

$\tan(A - B) = - 1$

This implies that,

$A - B = { \tan}^{ - 1} ( - 1)$

$A - B = { \tan}^{ - 1} ( 1) + 90$

$A - B = 45+ 90$

$A - B = 135 \degree$