Question

Given that A is obtuse and B is reflex angles and sin A=12/13 and cosB=3/5 without using calculators, evaluate tan(A+B)

Answer 1

$Sin\space A=\frac{12}{13}$

A is obtuse, A lie in the 2^nd quadrant

$Tan\space A=-\frac{12}{5}$

B is a reflex angle (B lie in 3^{rd or} 4^thquadrant

$Cos\space B=\frac{3}{5}$

Cos B is positive hence B lie in 4th quadrant.

$Tan\space B=-\frac{4}{3}$

$Tin\space( A+B)=\frac{Tan\space A Tan \space B}{1-Tan \space ATan \space B}=\frac{\frac{-12}{5}\frac{-4}{3}}{1-(\frac{-12}{5})(\frac{-4}{3})}$

$=\frac{\frac{-56}{15}}{\frac{-33}{15}}\\=\frac{56}{33}$