Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

$\cos A=-\frac{12}{13}\Rightarrow \frac{\pi }{2}<A<\pi ,\tan A=-\frac{5}{12}$, and $C=\pi -A$ gives $\tan C=\frac{5}{12}$. $\tan B=\frac{4}{3}\Rightarrow 0<B<\frac{\pi }{2},\cos B=\frac{3}{5}$, and $D=\pi -B$ gives $\cos D=-\frac{3}{5}$. Required equation: $x^2-\left(\frac{5}{12}-\frac{3}{5}\right)x+\frac{5}{12}\left(-\frac{3}{5}\right)=0\Rightarrow 60x^2+11x-15=0$